(* Content-type: application/vnd.wolfram.cdf.text *)

(*** Wolfram CDF File ***)
(* http://www.wolfram.com/cdf *)

(* CreatedBy='Mathematica 8.0' *)

(*************************************************************************)
(*                                                                       *)
(*  The Mathematica License under which this file was created prohibits  *)
(*  restricting third parties in receipt of this file from republishing  *)
(*  or redistributing it by any means, including but not limited to      *)
(*  rights management or terms of use, without the express consent of    *)
(*  Wolfram Research, Inc.                                               *)
(*                                                                       *)
(*************************************************************************)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       835,         17]
NotebookDataLength[    283150,       7436]
NotebookOptionsPosition[    265183,       6888]
NotebookOutlinePosition[    265844,       6910]
CellTagsIndexPosition[    265801,       6907]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell["Derivaci\[OAcute]n", "Title",
 CellChangeTimes->{{3.402221900287321*^9, 3.402221926909873*^9}, {
   3.40275716428125*^9, 3.402757177328125*^9}, {3.403330700391478*^9, 
   3.403330706124502*^9}, 3.404975418375*^9, 3.5581919694451027`*^9, {
   3.5591301646762185`*^9, 3.559130170822629*^9}, {3.559738654177397*^9, 
   3.559738664598298*^9}, {3.5610188519822817`*^9, 3.5610188697506995`*^9}, 
   3.561213876607561*^9}],

Cell[CellGroupData[{

Cell[TextData[{
 "Guillermo S\[AAcute]nchez (",
 ButtonBox["http://diarium.usal.es/guillermo",
  BaseStyle->"Hyperlink",
  ButtonData->{
    URL["http://diarium.usal.es/guillermo"], None},
  ButtonNote->"http://diarium.usal.es/guillermo"],
 ")"
}], "ItemParagraph",
 CellChangeTimes->{{3.4817991669102297`*^9, 3.48179917634823*^9}, {
  3.50652102881168*^9, 3.5065210329479165`*^9}, {3.506616173311325*^9, 
  3.506616182905342*^9}, {3.50661660323248*^9, 3.506616628130124*^9}, {
  3.5096080657618456`*^9, 3.5096080703794537`*^9}, {3.6007808317820764`*^9, 
  3.6007809022559795`*^9}}],

Cell["\<\
Departamento de Economia e H\.aa Econ\[OAcute]mica. Universidad de Salamanca. \
\>", "ItemParagraph",
 CellChangeTimes->{{3.5492836900858545`*^9, 3.5492837020822754`*^9}, {
  3.5587046622892094`*^9, 3.558704692631581*^9}, {3.558704744049791*^9, 
  3.558704762364413*^9}}],

Cell["Actualizado : 2012-11-25", "ItemParagraph",
 CellChangeTimes->{{3.5587047029744205`*^9, 3.5587047319752617`*^9}, {
  3.5587894054583817`*^9, 3.5587894068024983`*^9}, {3.55913017689104*^9, 
  3.559130178513443*^9}, {3.559487251560135*^9, 3.5594872521382637`*^9}, {
  3.5597386480621405`*^9, 3.5597386500277576`*^9}, {3.5603185864610233`*^9, 
  3.5603185871474237`*^9}, {3.5611213150384026`*^9, 3.5611213177372336`*^9}, {
  3.561210345469369*^9, 3.5612103464365845`*^9}, {3.561982338639533*^9, 
  3.561982341564026*^9}, {3.562045800970466*^9, 3.5620458021386137`*^9}, {
  3.5628244176943407`*^9, 3.5628244198627005`*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell["Sobre el estilo utilizado", "Subsubsection",
 CellChangeTimes->{{3.5591138036466403`*^9, 3.559113823957876*^9}, 
   3.55913018261625*^9}],

Cell[TextData[{
 StyleBox["Mathematica",
  FontSlant->"Italic"],
 " las salidas (",
 StyleBox["Input",
  FontSlant->"Italic"],
 ") por defecto las muestra utilizando el estilo: ",
 Cell[BoxData[
  ButtonBox["StandardForm",
   BaseStyle->"Link",
   ButtonData->"paclet:ref/StandardForm"]]],
 ". En su lugar preferiamos utilizar el estilo ",
 Cell[BoxData[
  ButtonBox["TraditionalForm",
   BaseStyle->"Link",
   ButtonData->"paclet:ref/TraditionalForm"]]],
 " que da una apariencia a las salidas (",
 StyleBox["Output",
  FontSlant->"Italic"],
 ") coincidente con el habitualmente utilizado en la notaci\[OAcute]n cl\
\[AAcute]sica utilizada en las matem\[AAcute]ticas. Esto puede hacerse para \
cada celda a\[NTilde]adiendo  // TraditionalForm al final de cada ",
 StyleBox["input",
  FontSlant->"Italic"],
 " . Sin embargo puede hacerse que este estilo (TraditionalForm) se aplique a \
todas las salidas  del cuaderno (o notebook) a\[NTilde]adiendo la siguiente \
sentencia (en este caso hemos definido la celda para que se ejecute \
automaticamente al inicio): "
}], "Text",
 CellChangeTimes->{{3.5584222350117645`*^9, 3.5584223439945416`*^9}, {
  3.5584466186725745`*^9, 3.5584466413552265`*^9}, {3.5584466950978155`*^9, 
  3.558446874671383*^9}, {3.558447123400505*^9, 3.558447293645172*^9}, {
  3.558447809215158*^9, 3.558447824924508*^9}, {3.558788054753585*^9, 
  3.5587881578428593`*^9}, {3.5587897243003335`*^9, 3.5587898877083592`*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"SetOptions", "[", 
   RowBox[{
    RowBox[{"EvaluationNotebook", "[", "]"}], ",", 
    RowBox[{"CommonDefaultFormatTypes", " ", "->", " ", 
     RowBox[{"{", 
      RowBox[{"\"\<Output\>\"", " ", "->", " ", "TraditionalForm"}], 
      "}"}]}]}], "]"}], " "}]], "Input",
 InitializationCell->True,
 CellChangeTimes->{{3.5584222350117645`*^9, 3.558422276243001*^9}, {
  3.5584223348685246`*^9, 3.558422349532604*^9}}],

Cell[TextData[{
 "Recuerde que las entradas debe escribirlas en ",
 Cell[BoxData[
  FormBox["StandardForm", TraditionalForm]]],
 ". Una vez que compruebe que funciona puede convertir la celda al  estilo \
tradicional marcando la celda y en la barra de menu elija ",
 Cell[BoxData[
  FormBox[
   RowBox[{"Cell", " ", "\[DoubleRightArrow]", 
    RowBox[{"Convert", " ", "to"}], " ", "\[DoubleRightArrow]", 
    "TradicionalForm"}], TraditionalForm]]],
 "."
}], "Text",
 CellFrame->0.5,
 CellChangeTimes->{{3.5619901744971857`*^9, 3.5619902180718956`*^9}, {
  3.561990251427689*^9, 3.5619902792605867`*^9}, {3.561990335520235*^9, 
  3.561990518970523*^9}, {3.5619906005933847`*^9, 3.5619906063500433`*^9}}],

Cell[TextData[{
 "En este cuaderno muchas entradas se muestran en el estilo tradicional. Para \
ver como originalmente han sido introducidas es muy recomendable que las vea \
en el estilo est\[AAcute]ndar, esto pude hacerlo marcando la celda y en la \
barra de menu elija ",
 Cell[BoxData[
  FormBox[
   RowBox[{"Cell", " ", "\[DoubleRightArrow]", 
    RowBox[{"Convert", " ", "to"}], " ", "\[DoubleRightArrow]", 
    "StandardForm"}], TraditionalForm]]],
 "."
}], "Text",
 CellFrame->0.5,
 CellChangeTimes->{{3.5619901744971857`*^9, 3.5619902180718956`*^9}, {
  3.561990251427689*^9, 3.5619902792605867`*^9}, {3.561990335520235*^9, 
  3.561990419828074*^9}, {3.561990521326228*^9, 3.5619906222003546`*^9}, {
  3.56199067519588*^9, 3.561990745366479*^9}}],

Cell["\<\
A lo largo de este cuaderno introduciremos de vez en cuando la instrucci\
\[OAcute]n\
\>", "Subitem",
 CellChangeTimes->{{3.562043985836162*^9, 3.56204401408873*^9}}],

Cell[BoxData[
 RowBox[{"Clear", "[", "\"\<Global`*\>\"", "]"}]], "Input",
 CellID->38138293],

Cell["Esto se hace para borrar definiciones previas. Por ejemplo:", "Subitem",
 CellChangeTimes->{{3.562044018171254*^9, 3.5620440474559984`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"y", " ", "=", "3"}]], "Input",
 CellChangeTimes->{{3.5620440521156445`*^9, 3.5620440560821476`*^9}}],

Cell[BoxData[
 FormBox["3", TraditionalForm]], "Output",
 CellChangeTimes->{3.5620440599596186`*^9}]
}, Open  ]],

Cell["Si utiliza de nuevo y, entonces y se sustituira por y = 3", "Subitem",
 CellChangeTimes->{{3.5620441052593994`*^9, 3.562044128232388*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  SuperscriptBox["y", "2"], " "}]], "Input",
 CellChangeTimes->{{3.562044078154974*^9, 3.5620440973544397`*^9}}],

Cell[BoxData[
 FormBox["9", TraditionalForm]], "Output",
 CellChangeTimes->{3.5620441014709187`*^9, 3.5620442491018543`*^9}]
}, Open  ]],

Cell[TextData[{
 "A veces quiere emplear  el s\[IAcute]mbolo ",
 Cell[BoxData[
  FormBox["y", TraditionalForm]]],
 " de nuevo en ese caso utilice: "
}], "Subitem",
 CellChangeTimes->{{3.5620441324399023`*^9, 3.5620442137763042`*^9}, {
  3.5620442568808107`*^9, 3.562044263624673*^9}}],

Cell[BoxData[
 RowBox[{"Clear", "[", "\"\<Global`*\>\"", "]"}]], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  SuperscriptBox["y", "2"], " "}]], "Input",
 CellChangeTimes->{{3.562044078154974*^9, 3.5620440973544397`*^9}}],

Cell[BoxData[
 FormBox[
  SuperscriptBox["y", "2"], TraditionalForm]], "Output",
 CellChangeTimes->{3.5620442491868186`*^9}]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell["Concepto de derivada", "Section",
 CellChangeTimes->{{3.561013799296636*^9, 3.561013802494676*^9}, {
  3.561014136683163*^9, 3.561014144656829*^9}, {3.5611217824269567`*^9, 
  3.561121796014717*^9}}],

Cell[TextData[{
 "Antes de empezar recuerde que si define una funci\[OAcute]n ",
 Cell[BoxData[
  FormBox[
   RowBox[{"f", 
    RowBox[{"(", "x", ")"}]}], TraditionalForm]]],
 ", si asigna a x un valor ",
 Cell[BoxData[
  FormBox["a", TraditionalForm]]],
 " lo que se har\[AAcute] es sustituir x por ese valor a. Por ejemplo: Sea \
f(x) = ",
 Cell[BoxData[
  FormBox[
   SuperscriptBox["x", "2"], TraditionalForm]]],
 " entonces para x= 3 se denota: f(3) = ",
 Cell[BoxData[
  FormBox[
   SuperscriptBox["3", "2"], TraditionalForm]]],
 " = 9. Este mismo criterio se aplica cuando en f(x) en vez de un valor ",
 Cell[BoxData[
  FormBox["a", TraditionalForm]]],
 " asigamos a x una expresi\[OAcute]n ",
 StyleBox["expr.",
  FontSlant->"Italic"],
 "  Por ejemplo: si en caso anterior en vez de a tenemos cos x, entonces \
f(cos x) = ",
 Cell[BoxData[
  FormBox[
   SuperscriptBox[
    RowBox[{"(", 
     RowBox[{"cos", " ", "x"}], ")"}], "2"], TraditionalForm]]]
}], "Text",
 CellChangeTimes->{{3.562041783028245*^9, 3.5620423755680304`*^9}, {
  3.5620424061209416`*^9, 3.56204245031363*^9}, {3.5620427918272967`*^9, 
  3.5620428311773634`*^9}}],

Cell["\<\
Mostramos como se construye con Mathematica el ejemplo anterior. Observe que \
el argumento de la funci\[OAcute]n se escribe entre corcheres, en lugar de \
parentesis. El m\[EAcute]todo es aplicable a cualquier funci\[OAcute]n \
\>", "Subitem",
 CellChangeTimes->{{3.562042491332883*^9, 3.562042525743247*^9}, {
  3.5620425609198*^9, 3.562042677391657*^9}, {3.5620427147995014`*^9, 
  3.5620427690163784`*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"f", "[", "x_", "]"}], ":=", 
  SuperscriptBox["x", "2"]}]], "Input",
 CellChangeTimes->{{3.562042619123198*^9, 3.5620426347361937`*^9}, {
  3.562042681944271*^9, 3.5620426884101353`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"f", "[", "3", "]"}]], "Input",
 CellChangeTimes->{{3.562042700512644*^9, 3.5620427014887505`*^9}, {
  3.56204291090556*^9, 3.5620429132808695`*^9}}],

Cell[BoxData[
 FormBox["9", TraditionalForm]], "Output",
 CellChangeTimes->{3.5620427793797126`*^9, 3.5620428466363616`*^9, 
  3.5620429139149933`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"f", "[", 
  RowBox[{"Cos", "[", "x", "]"}], "]"}]], "Input",
 CellChangeTimes->{{3.5620427047451878`*^9, 3.5620427096577854`*^9}, {
  3.562042840225546*^9, 3.562042841864708*^9}}],

Cell[BoxData[
 FormBox[
  RowBox[{
   SuperscriptBox["cos", "2"], "(", "x", ")"}], TraditionalForm]], "Output",
 CellChangeTimes->{3.5620427794327602`*^9, 3.5620428466883945`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"f", "[", 
  RowBox[{"x", "+", "\[CapitalDelta]x"}], "]"}]], "Input",
 CellChangeTimes->{{3.562042877225275*^9, 3.562042890600995*^9}}],

Cell[BoxData[
 FormBox[
  SuperscriptBox[
   RowBox[{"(", 
    RowBox[{"\[CapitalDelta]x", "+", "x"}], ")"}], "2"], 
  TraditionalForm]], "Output",
 CellChangeTimes->{3.5620428938633857`*^9}]
}, Open  ]],

Cell[TextData[{
 "Sea f (x), se define derivada  ( denotado f\[CloseCurlyQuote](y) o ",
 Cell[BoxData[
  FormBox[
   FractionBox[
    StyleBox["df",
     FontSlant->"Italic"], "dx"], TraditionalForm]]],
 "o Df) a "
}], "Text",
 CellChangeTimes->{{3.561211090292079*^9, 3.5612112297391634`*^9}}],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    RowBox[{"f", " ", "'"}], 
    RowBox[{"(", "x", ")"}]}], "=", 
   RowBox[{
    RowBox[{
     UnderscriptBox["lim", 
      RowBox[{"x", "\[Rule]", "a"}]], "\[ThinSpace]", 
     FractionBox[
      RowBox[{
       RowBox[{"f", "(", "x", ")"}], "-", 
       RowBox[{"f", "(", "a", ")"}]}], 
      RowBox[{"x", "-", "a"}]]}], "=", 
    RowBox[{
     UnderscriptBox["lim", 
      RowBox[{"\[CapitalDelta]x", "\[Rule]", "0"}]], "\[ThinSpace]", 
     FractionBox[
      RowBox[{
       RowBox[{"f", "(", 
        RowBox[{"x", "+", "\[CapitalDelta]x"}], ")"}], "-", 
       RowBox[{"f", "(", "x", ")"}]}], "\[CapitalDelta]x"]}]}]}], 
  TraditionalForm]], "Text",
 CellChangeTimes->{{3.5612107823038387`*^9, 3.561210782952946*^9}, {
   3.5612108180094957`*^9, 3.561210939461776*^9}, 3.5612109956786475`*^9, {
   3.5612112507199926`*^9, 3.5612113270000715`*^9}, {3.5612117305399036`*^9, 
   3.561211818867133*^9}, {3.562045259859214*^9, 3.562045273878961*^9}}],

Cell["\<\
Observe en el gr\[AAcute]fico que la definici\[OAcute]n anterior equivale a \
construir un triangulo cuya base x-a la va haciendo cada vez mas peque\
\[NTilde]a.\
\>", "Text",
 CellChangeTimes->{{3.56204536029602*^9, 3.562045383160999*^9}, {
  3.562045414561962*^9, 3.5620455114423685`*^9}}],

Cell[BoxData[
 GraphicsBox[{{{}, {}, 
    {GrayLevel[0], Thickness[Large], LineBox[CompressedData["
1:eJwd1Xs0FHgbB/AxLmlQLiHMuI0o13SRdlvPI4QIiVy2lEno5nawkUIRamlE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      "]]}, 
    {RGBColor[0, 0.6, 0.4], AbsoluteThickness[1.5], LineBox[CompressedData["
1:eJwB4QIe/SFib1JlAgAAAC0AAAACAAAAnX5iBjFkiz4nNuUj5pb7P8TTIExX
IGk/oGcM9T+h+z//xr6DICB5PxiZM8aZq/s/ncCNHwUgiT8K/IFoTcD7P2w9
dW33H5k/7cEerbTp+z/T+2iU8B+pP7NNWDaDPPw/B9viJ+0fuT8/ZctIIOL8
P6HKn3HrH8k/V5SxbVot/j+ur4nbbC7aPwEje8jDfQBAZz/Rmexy4z9mDLWI
Ds0BQG7lKeO0ruk/FmQ9jMUVA0AKIYQn3zjwP4LlgfxYegRAjhDLKqFg8z9/
912bIMcFQGLbVL8DzPY/OTP2psQvB0BxxYRibyf6Pzzd3PXUkQhAsXAMUxhJ
/T/QF1tzGdwJQKF7a+owVwBAIXyVXTpCC0CCn/xR9OwBQAJxZ3aPkAxAANPg
QLx6A0As1IfSUNgNQCZ0ZnhUKgVAFGFkm+47D0Dk9ZdWC70GQEY/bEngQxBA
SuVqfZJxCEDgYoR7t/cQQE7kkCseHgpAoL1Dz0SoEUDqw2KAyK0LQKfgTjrs
TBJALhHWHUNfDUCNGLjbgf8SQAo/9WHc8w5AuxhtlDGmE0BH7Vr3IlUQQMct
gIPPWhRA2MJkAVosEUD4eTqUIwwVQLWIxF4g9RFAco5AvJGxFUBmBXXgzs4S
QMq3pBruZBZAY3J7tQyaE0BqqVSQZAwXQC9nK85MYRRALtKrJ5GwF0DPEiwL
dTkVQNIPYfWrYhhAu66CmywDFkC9FWLa4AgZQHsBKlDM3RZAhzDB9QO9GUAK
3HpIbrQXQHaCxzLdbRpA5aYhlJ98GECsnBmH0BIbQJQoGQS5VRlAwsvJEbLF
G0CQmmbHYSAaQCDDxbOtbBxAWpRdzgznGkCi8Wh3XxAdQPhEpfmfvhtAAzVq
cf/BHUDj5UJ4woccQK1At4K5Zx5Aoj0xG81hHUA1YWLKYRsfQK2FdRFnLR5A
BUpZKSTDH0AxzjWTQ3ceQAAAAAAAACBArs81ww==
      "]]}, 
    {RGBColor[0.8, 0, 0.4], Thickness[Large], LineBox[CompressedData["
1:eJwBgQF+/iFib1JlAgAAABcAAAACAAAAnX5iBjFkiz5MheKasaL4v8TTIExX
IGk/NHpJvAF9+L//xr6DICB5PyBvsN1RV/i/ncCNHwUgiT/wWH4g8gv4v2w9
dW33H5k/lCwapjJ197/T+2iU8B+pP9jTUbGzR/a/B9viJ+0fuT9kIsHHtezz
v6HKn3HrH8k/8H4/6XNt7r+ur4nbbC7aP8CeUWqC/9O/Zz/Rmexy4z+Yzvid
wibSP27lKeO0ruk/YFkGK7rG6z8KIYQn3zjwP6q3UDfrB/g/jhDLKqFg8z8b
w5KgmL8AQGLbVL8DzPY/WXNhf6zgBUBxxYRibyf6P3BSKfTN6QpAsXAMUxhJ
/T9Q0/RcS5wPQKF7a+owVwBAlE7SzxxaEkCCn/xR9OwBQGYELOvBuhRAANPg
QLx6A0CjUYLRbQ8XQCZ0ZnhUKgVAXMPKJNKWGUDk9ZdWC70GQPkFFXLk8htA
SuVqfZJxCEASbVEsr4EeQOnxiQpzcAlAAAAAAAAAIEBo7rJ+
      "]]}}, {
    {GrayLevel[0], 
     InsetBox["\<\"\\!\\(\\*\\nStyleBox[\\\"O\\\",\\nFontSlant->\\\"Italic\\\"\
]\\)\"\>", {0, 0}, {1.5, 1.5}], 
     InsetBox["\<\"\\!\\(\\*FormBox[\\n RowBox[{\\\"y\\\", \\\"=\\\", \\n  \
RowBox[{\\\"f\\\", \\\"(\\\", \\\"x\\\", \\\")\\\"}]}],\\n \
TraditionalForm]\\)\"\>", {10, 7.295836866004329}, {1, 3}], 
     InsetBox["\<\"\\!\\(\\*FormBox[\\n RowBox[{\\n  RowBox[{\\\"f\\\", \\\"(\
\\\", \\\"x\\\", \\\")\\\"}], \\\"-\\\", \\n  RowBox[{\\\"f\\\", \\\"(\\\", \
\\\"a\\\", \\\")\\\"}]}],\\n TraditionalForm]\\)\"\>", \
{5.5, 4.6081976621622465`}, {-1.1, 0}], 
     InsetBox["\<\"\\!\\(\\*FormBox[\\n RowBox[{\\\"x\\\", \\\"-\\\", \\\"a\\\
\"}],\\n TraditionalForm]\\)\"\>", {3.5, 2.960279229160082}, {0, 1.5}], 
     InsetBox["\<\"\\!\\(\\*FormBox[\\\"P\\\",\\n TraditionalForm]\\)\"\>", \
{1.5, 2.960279229160082}, {1.5, -1.5}], 
     InsetBox["\<\"\\!\\(\\*FormBox[\\\"Q\\\",\\n TraditionalForm]\\)\"\>", \
{5.5, 6.256116095164411}, {-1.5, -1.5}], InsetBox[
      FrameBox[
       PaneBox["\<\"\\!\\(\\*FormBox[\\n RowBox[{SubscriptBox[\\\"m\\\", \
\\\"tan\\\"], \\\"=\\\", \\n  RowBox[{SubscriptBox[\\\"lim\\\", \\n    \
RowBox[{\\\"x\\\", \\\"\[Rule]\\\", \\\"a\\\"}]], FractionBox[\\n    RowBox[{\
\\n     RowBox[{\\\"f\\\", \\\"(\\\", \\\"x\\\", \\\")\\\"}], \\\"-\\\", \\n  \
   RowBox[{\\\"f\\\", \\\"(\\\", \\\"a\\\", \\\")\\\"}]}], \\n    \
RowBox[{\\\"x\\\", \\\"-\\\", \\\"a\\\"}]]}]}],\\n TraditionalForm]\\)\"\>",
        BaseStyle->{
         LineIndent -> 0, LinebreakAdjustments -> {1, 1, 0, 0, 0}, 
          LineBreakWithin -> Automatic, Hyphenation -> True, TextAlignment -> 
          Left, FontSize -> 13}],
       Background->GrayLevel[1],
       FrameStyle->GrayLevel[0.85],
       RoundingRadius->5,
       StripOnInput->False], {4.01324025694664, 10.5}, {0, 1}], InsetBox[
      FrameBox[
       PaneBox["\<\"\\!\\(\\*FormBox[\\n RowBox[{SubscriptBox[\\\"m\\\", \
\\\"sec\\\"], \\\"=\\\", FractionBox[\\n   RowBox[{\\n    RowBox[{\\\"f\\\", \
\\\"(\\\", \\\"x\\\", \\\")\\\"}], \\\"-\\\", \\n    RowBox[{\\\"f\\\", \\\"(\
\\\", \\\"a\\\", \\\")\\\"}]}], \\n   RowBox[{\\\"x\\\", \\\"-\\\", \
\\\"a\\\"}]]}],\\n TraditionalForm]\\)\"\>",
        BaseStyle->{
         LineIndent -> 0, LinebreakAdjustments -> {1, 1, 0, 0, 0}, 
          LineBreakWithin -> Automatic, Hyphenation -> True, TextAlignment -> 
          Left, FontSize -> 13}],
       Background->GrayLevel[1],
       FrameStyle->GrayLevel[0.85],
       RoundingRadius->5,
       StripOnInput->False], {6.402816413650265, 7}, {-0.5, -1.25}]}, 
    {RGBColor[0.8, 0, 0.4], AbsoluteThickness[1], 
     LineBox[{{1.5, 2.960279229160082}, {5.5, 2.960279229160082}, {5.5, 
      6.256116095164411}}], 
     {Dashing[{Small, Small}], 
      LineBox[{{1.5, 2.960279229160082}, {0, 2.960279229160082}}], 
      LineBox[{{1.5, 0}, {1.5, 2.960279229160082}}], 
      LineBox[{{5.5, 0}, {5.5, 2.960279229160082}}], 
      LineBox[{{5.5, 6.256116095164411}, {0, 6.256116095164411}}]}, 
     {AbsoluteThickness[4], Opacity[0.5], Dashing[{}], 
      ArrowBox[{{5.5, 0}, {4.5, 0}}], 
      ArrowBox[{{0, 6.256116095164411}, {0, 5.256116095164411}}], 
      {RGBColor[0, 0.4, 0.8], AbsolutePointSize[7], Opacity[1], 
       PointBox[{1.5, 2.960279229160082}], 
       PointBox[{5.5, 6.256116095164411}]}}}}},
  AspectRatio->1,
  Axes->True,
  AxesLabel->{
    FormBox[
    "\"\\!\\(\\*FormBox[\\\"x\\\",\\n TraditionalForm]\\)\"", 
     TraditionalForm], 
    FormBox[
    "\"\\!\\(\\*FormBox[\\\"y\\\",\\n TraditionalForm]\\)\"", 
     TraditionalForm]},
  AxesOrigin->{0, 0},
  AxesStyle->Arrowheads[{0, 0.04}],
  BaseStyle->{"Text", 13},
  ImageSize->360,
  PlotRange->{{-1.5, 10}, {-1, 11}},
  PlotRangeClipping->True,
  PlotRangePadding->{Automatic, Automatic},
  Ticks->{{{1.5, 
      FormBox[
      "\"\\!\\(\\*FormBox[\\\"a\\\",\\n TraditionalForm]\\)\"", 
       TraditionalForm]}, {5.5, 
      FormBox[
      "\"\\!\\(\\*FormBox[\\\"x\\\",\\n TraditionalForm]\\)\"", 
       TraditionalForm]}}, {{2.960279229160082, 
      FormBox[
      "\"\\!\\(\\*FormBox[\\n RowBox[{\\\"f\\\", \\\"(\\\", \\\"a\\\", \
\\\")\\\"}],\\n TraditionalForm]\\)\"", TraditionalForm]}, {6.256116095164411, 
      FormBox[
      "\"\\!\\(\\*FormBox[\\n RowBox[{\\\"f\\\", \\\"(\\\", \\\"x\\\", \
\\\")\\\"}],\\n TraditionalForm]\\)\"", TraditionalForm]}}}]], "Text",
 CellChangeTimes->{3.5620452398206778`*^9}],

Cell[TextData[{
 "Suponga que en el grafico f(x) = ",
 Cell[BoxData[
  FormBox[
   SuperscriptBox["x", "2"], TraditionalForm]]],
 " y quiere calcular la derivada en ",
 Cell[BoxData[
  FormBox[
   RowBox[{"a", "=", "5"}], TraditionalForm]]],
 " aplicando la definici\[OAcute]n. Partiramos de ",
 Cell[BoxData[
  RowBox[{
   FractionBox[
    RowBox[{
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{"5", "+", "\[CapitalDelta]x"}], ")"}], "2"], "-", 
     SuperscriptBox["5", "2"]}], "\[CapitalDelta]x"], " "}]]],
 " y vamos disminuyendo \[CapitalDelta]x y vemos que cuando  \[CapitalDelta]x\
\[RightArrow]0 entonces  f \[OpenCurlyQuote](5) = 10"
}], "Text",
 CellChangeTimes->{{3.561990833820747*^9, 3.561990864132324*^9}, {
  3.561991032242234*^9, 3.5619910644570603`*^9}, {3.5619911182936945`*^9, 
  3.561991137029175*^9}, {3.5619911873076525`*^9, 3.5619912081335187`*^9}, {
  3.562041672062991*^9, 3.562041721526346*^9}, {3.5620455306618724`*^9, 
  3.5620455737223387`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Manipulate", "[", 
  RowBox[{
   FractionBox[
    RowBox[{
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{"5", "+", "\[CapitalDelta]x"}], ")"}], "2"], "-", 
     SuperscriptBox["5", "2"]}], "\[CapitalDelta]x"], ",", " ", 
   RowBox[{"{", 
    RowBox[{"\[CapitalDelta]x", ",", " ", "0.01", ",", " ", "0.00001"}], 
    "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.5612107823038387`*^9, 3.561210782952946*^9}, {
   3.5612108180094957`*^9, 3.561210939461776*^9}, 3.5612109956786475`*^9, {
   3.5612113611516104`*^9, 3.561211395169794*^9}, {3.5619008639006124`*^9, 
   3.561900867192252*^9}, 3.561983583566167*^9, {3.5619837713805866`*^9, 
   3.561983779524048*^9}, {3.5619909000912457`*^9, 3.5619910053939457`*^9}, {
   3.5619910845815763`*^9, 3.561991094799838*^9}}],

Cell[BoxData[
 FormBox[
  TagBox[
   FormBox[
    StyleBox[
     DynamicModuleBox[{$CellContext`\[CapitalDelta]x$$ = 0.00001, 
      Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, 
      Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ =
       1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{
        Hold[$CellContext`\[CapitalDelta]x$$], 0.01, 0.00001}}, 
      Typeset`size$$ = {30., {0., 16.}}, Typeset`update$$ = 0, 
      Typeset`initDone$$, Typeset`skipInitDone$$ = 
      True, $CellContext`\[CapitalDelta]x$1146$$ = 0}, 
      DynamicBox[Manipulate`ManipulateBoxes[
       1, TraditionalForm, 
        "Variables" :> {$CellContext`\[CapitalDelta]x$$ = 0.01}, 
        "ControllerVariables" :> {
          
          Hold[$CellContext`\[CapitalDelta]x$$, \
$CellContext`\[CapitalDelta]x$1146$$, 0]}, 
        "OtherVariables" :> {
         Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, 
          Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, 
          Typeset`specs$$, Typeset`size$$, Typeset`update$$, 
          Typeset`initDone$$, Typeset`skipInitDone$$}, 
        "Body" :> ((5 + $CellContext`\[CapitalDelta]x$$)^2 - 
          5^2)/$CellContext`\[CapitalDelta]x$$, 
        "Specifications" :> {{$CellContext`\[CapitalDelta]x$$, 0.01, 
           0.00001}}, "Options" :> {}, "DefaultOptions" :> {}],
       ImageSizeCache->{523., {98., 111.}},
       SingleEvaluation->True],
      Deinitialization:>None,
      DynamicModuleValues:>{},
      SynchronousInitialization->True,
      UnsavedVariables:>{Typeset`initDone$$},
      UntrackedVariables:>{Typeset`size$$}], "Manipulate",
     Deployed->True,
     StripOnInput->False],
    TraditionalForm],
   Manipulate`InterpretManipulate[1]], TraditionalForm]], "Output",
 CellChangeTimes->{3.5619910104016743`*^9, 3.561991098060322*^9}]
}, {2}]],

Cell[TextData[{
 "Podemos deducir una formula general que nos permita calcular la derivada de \
",
 Cell[BoxData[
  FormBox[
   SuperscriptBox["x", "2"], TraditionalForm]]],
 " para cualquier valor de x"
}], "Text",
 CellChangeTimes->{{3.5619912134062853`*^9, 3.5619912549176188`*^9}}],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    UnderscriptBox["lim", 
     RowBox[{"\[CapitalDelta]x", "\[Rule]", "0"}]], "\[ThinSpace]", 
    FractionBox[
     RowBox[{
      SuperscriptBox[
       RowBox[{"(", 
        RowBox[{"x", "+", "\[CapitalDelta]x"}], ")"}], "2"], "-", 
      SuperscriptBox["x", "2"]}], "\[CapitalDelta]x"]}], "=", 
   RowBox[{
    RowBox[{
     UnderscriptBox["lim", 
      RowBox[{"\[CapitalDelta]x", "\[Rule]", "0"}]], 
     FractionBox[
      RowBox[{
       RowBox[{"(", 
        RowBox[{
         SuperscriptBox["x", "2"], "+", 
         RowBox[{"2", " ", "x", " ", "\[CapitalDelta]x"}], "-", " ", 
         SuperscriptBox["\[CapitalDelta]x", "2"]}], ")"}], "-", 
       SuperscriptBox["x", "2"]}], "\[CapitalDelta]x"]}], "=", 
    RowBox[{
     RowBox[{
      UnderscriptBox["lim", 
       RowBox[{"\[CapitalDelta]x", "\[Rule]", "0"}]], 
      FractionBox[
       RowBox[{
        RowBox[{"2", " ", "x", " ", "\[CapitalDelta]x"}], "-", " ", 
        SuperscriptBox["\[CapitalDelta]x", "2"]}], "\[CapitalDelta]x"]}], "=", 
     RowBox[{
      RowBox[{
       UnderscriptBox["lim", 
        RowBox[{"\[CapitalDelta]x", "\[Rule]", "0"}]], 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"2", " ", "x"}], " ", "-", " ", "\[CapitalDelta]x"}], 
        ")"}]}], "=", " ", 
      RowBox[{"2", " ", "x"}]}]}]}]}], TraditionalForm]], "Text",
 CellChangeTimes->{{3.5619008944769697`*^9, 3.561900901637452*^9}, {
  3.561900938719081*^9, 3.561901118807569*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 FormBox[
  RowBox[{
   UnderscriptBox["lim", 
    RowBox[{"\[CapitalDelta]x", "\[Rule]", "0"}]], "\[ThinSpace]", 
   FractionBox[
    RowBox[{
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{"\[CapitalDelta]x", "+", "x"}], ")"}], "2"], "-", 
     SuperscriptBox["x", "2"]}], "\[CapitalDelta]x"]}], 
  TraditionalForm]], "Input",
 CellChangeTimes->{{3.5612107823038387`*^9, 3.561210782952946*^9}, {
   3.5612108180094957`*^9, 3.561210939461776*^9}, 3.5612109956786475`*^9, {
   3.5612113611516104`*^9, 3.561211395169794*^9}, {3.5619008639006124`*^9, 
   3.561900867192252*^9}, 3.561983583566167*^9, {3.5619837713805866`*^9, 
   3.561983779524048*^9}, 3.562043043008557*^9, 3.5620430903225384`*^9, 
   3.5620431494480705`*^9}],

Cell[BoxData[
 FormBox[
  RowBox[{"2", " ", "x"}], TraditionalForm]], "Output",
 CellChangeTimes->{3.561900868034662*^9}]
}, Open  ]],

Cell[TextData[{
 "Recuerde: Para ver como originalmente ha sido introducidas la expresi\
\[OAcute]n anterior marca celda y en la barra de menu elija ",
 Cell[BoxData[
  FormBox[
   RowBox[{"Cell", " ", "\[DoubleRightArrow]", 
    RowBox[{"Convert", " ", "to"}], " ", "\[DoubleRightArrow]", 
    "StandardForm"}], TraditionalForm]]],
 ". Entonces observe que ",
 Cell[BoxData[
  FormBox[
   UnderscriptBox["lim", 
    RowBox[{"\[CapitalDelta]x", "\[Rule]", "0"}]], TraditionalForm]],
  CellChangeTimes->{{3.5612107823038387`*^9, 3.561210782952946*^9}, {
    3.5612108180094957`*^9, 3.561210939461776*^9}, 3.5612109956786475`*^9, {
    3.5612113611516104`*^9, 3.561211395169794*^9}, {3.5619008639006124`*^9, 
    3.561900867192252*^9}, 3.561983583566167*^9, {3.5619837713805866`*^9, 
    3.561983779524048*^9}, 3.562043043008557*^9, 3.5620430903225384`*^9, 
    3.5620431494480705`*^9}],
 " se escribe Limit[...,\[CapitalDelta]x\[Rule]0]. Una vez escrito puede \
convertirlo a la notaci\[OAcute]n tradicional  ",
 "marcando la celda y en la barra de menu elija ",
 Cell[BoxData[
  FormBox[
   RowBox[{"Cell", " ", "\[DoubleRightArrow]", 
    RowBox[{"Convert", " ", "to"}], " ", "\[DoubleRightArrow]", 
    "TradicionalForm"}], TraditionalForm]]],
 "."
}], "Text",
 CellFrame->0.5,
 CellChangeTimes->{{3.5619901744971857`*^9, 3.5619902180718956`*^9}, {
  3.561990251427689*^9, 3.5619902792605867`*^9}, {3.561990335520235*^9, 
  3.561990419828074*^9}, {3.561990521326228*^9, 3.5619906222003546`*^9}, {
  3.56199067519588*^9, 3.561990745366479*^9}, {3.5620429884565444`*^9, 
  3.5620432411708555`*^9}}],

Cell["\<\
La aplicamos a x = 5 , entonces 2 x = 10 , que es el resultado que antes \
habiamos obtenido.\
\>", "Text",
 CellChangeTimes->{{3.561991258848794*^9, 3.561991284541829*^9}, {
  3.5620432641437454`*^9, 3.56204330090348*^9}}],

Cell[CellGroupData[{

Cell[TextData[{
 "A partir de la definici\[OAcute]n de derivada calcular la derivada de ",
 Cell[BoxData[
  FormBox[
   SuperscriptBox["x", "n"], TraditionalForm]]],
 ", Sen x (en ingl\[EAcute]s Sin x) y ",
 " ",
 Cell[BoxData[
  FormBox[
   SuperscriptBox["\[ExponentialE]", 
    RowBox[{"-", "x"}]], TraditionalForm]]]
}], "Subsubsection",
 CellChangeTimes->{{3.561993297201765*^9, 3.5619933123340564`*^9}, {
  3.5619933458903017`*^9, 3.5619933658430853`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Limit", "[", 
  RowBox[{
   FractionBox[
    RowBox[{
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{"x", "+", " ", "\[CapitalDelta]x"}], ")"}], "n"], "-", 
     SuperscriptBox["x", "n"]}], "\[CapitalDelta]x"], ",", 
   RowBox[{"\[CapitalDelta]x", "\[Rule]", "0"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.5612107823038387`*^9, 3.561210782952946*^9}, {
   3.5612108180094957`*^9, 3.561210939461776*^9}, 3.5612109956786475`*^9, {
   3.5612113611516104`*^9, 3.561211395169794*^9}, {3.5619008639006124`*^9, 
   3.561900867192252*^9}, 3.561983583566167*^9, {3.5619837713805866`*^9, 
   3.561983779524048*^9}, {3.5619839883223476`*^9, 3.5619839928000927`*^9}, 
   3.561984024159912*^9, 3.5619840802955484`*^9, {3.561988818423558*^9, 
   3.5619888244296355`*^9}}],

Cell[BoxData[
 FormBox[
  RowBox[{"n", " ", 
   SuperscriptBox["x", 
    RowBox[{"n", "-", "1"}]]}], TraditionalForm]], "Output",
 CellChangeTimes->{3.561983995795658*^9, 3.5619885304120636`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Limit", "[", 
  RowBox[{
   FractionBox[
    RowBox[{
     RowBox[{"Sin", "[", 
      RowBox[{"\[CapitalDelta]x", "+", "x"}], "]"}], "-", 
     RowBox[{"Sin", "[", "x", "]"}]}], "\[CapitalDelta]x"], ",", 
   RowBox[{"\[CapitalDelta]x", "\[Rule]", "0"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.5612107823038387`*^9, 3.561210782952946*^9}, {
   3.5612108180094957`*^9, 3.561210939461776*^9}, 3.5612109956786475`*^9, {
   3.5612113611516104`*^9, 3.561211395169794*^9}, {3.5619008639006124`*^9, 
   3.561900867192252*^9}, 3.561983583566167*^9, {3.5619837713805866`*^9, 
   3.561983779524048*^9}, {3.5619839883223476`*^9, 3.5619839928000927`*^9}, 
   3.561984024159912*^9, {3.5619840802955484`*^9, 3.561984111218514*^9}, {
   3.561984232273656*^9, 3.5619842578593597`*^9}, 3.5619888308101172`*^9, {
   3.5619929647593727`*^9, 3.5619929925279064`*^9}}],

Cell[BoxData[
 FormBox[
  RowBox[{"cos", "(", "x", ")"}], TraditionalForm]], "Output",
 CellChangeTimes->{3.5619841304712586`*^9, 3.561984236470567*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Limit", "[", 
  RowBox[{
   FractionBox[
    RowBox[{
     SuperscriptBox["\[ExponentialE]", 
      RowBox[{"x", "+", " ", "\[CapitalDelta]x"}]], "-", 
     SuperscriptBox["\[ExponentialE]", "x"]}], "\[CapitalDelta]x"], ",", 
   RowBox[{"\[CapitalDelta]x", "\[Rule]", "0"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.5612107823038387`*^9, 3.561210782952946*^9}, {
   3.5612108180094957`*^9, 3.561210939461776*^9}, 3.5612109956786475`*^9, {
   3.5612113611516104`*^9, 3.561211395169794*^9}, {3.5619008639006124`*^9, 
   3.561900867192252*^9}, 3.561983583566167*^9, {3.5619837713805866`*^9, 
   3.561983779524048*^9}, {3.5619839883223476`*^9, 3.5619839928000927`*^9}, 
   3.561984024159912*^9, {3.5619840802955484`*^9, 3.561984111218514*^9}, {
   3.561984232273656*^9, 3.5619842578593597`*^9}, {3.5619843307780313`*^9, 
   3.5619843701229973`*^9}, {3.5619845252875595`*^9, 3.561984554554183*^9}, 
   3.5619888365821915`*^9}],

Cell[BoxData[
 FormBox[
  SuperscriptBox["\[ExponentialE]", "x"], TraditionalForm]], "Output",
 CellChangeTimes->{3.5619843741167765`*^9, 3.5619846945053716`*^9, 
  3.561984735690428*^9}]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell["\<\
Concepto geom\[EAcute]trico de derivada\
\>", "Subsubsection",
 CellChangeTimes->{{3.5619822560646105`*^9, 3.5619822717828074`*^9}}],

Cell[TextData[{
 "La derivada de una funci\[OAcute]n f(x) en un punto ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "0"], TraditionalForm]]],
 " podemos interpretarla como la recta tangente en ese punto. Compruebelo en \
el grafico anterior: Observe que en el punto P la derivada corresponde a la \
tangente a la funci\[OAcute]n en ese punto.\nEn efecto como ",
 Cell[BoxData[
  RowBox[{
   RowBox[{
    RowBox[{"f", " ", "'"}], 
    RowBox[{"(", "x", ")"}]}], "=", 
   RowBox[{
    UnderscriptBox["lim", 
     RowBox[{"x", "\[Rule]", 
      SubscriptBox["x", "0"]}]], "\[ThinSpace]", 
    FractionBox[
     RowBox[{
      RowBox[{"f", "(", "x", ")"}], "-", 
      RowBox[{"f", "(", 
       SubscriptBox["x", "0"], ")"}]}], 
     RowBox[{"x", "-", 
      SubscriptBox["x", "0"]}]]}]}]],
  CellChangeTimes->{{3.5612107823038387`*^9, 3.561210782952946*^9}, {
    3.5612108180094957`*^9, 3.561210939461776*^9}, 3.5612109956786475`*^9, {
    3.5612112507199926`*^9, 3.5612113270000715`*^9}, {3.5612117305399036`*^9, 
    3.561211818867133*^9}}],
 " esto es: ",
 Cell[BoxData[
  FormBox[
   RowBox[{"f", 
    RowBox[{"(", "x", ")"}]}], TraditionalForm]]],
 " = ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    RowBox[{"f", "(", 
     SubscriptBox["x", "0"], ")"}], "+", 
    RowBox[{
     RowBox[{"f", "'"}], 
     RowBox[{"(", "x", ")"}], " ", 
     RowBox[{"(", 
      RowBox[{"x", "-", 
       SubscriptBox["x", "0"]}], ")"}]}]}], TraditionalForm]]],
 ". \nque la ecuaci\[OAcute]n de una recta Y = A + m X donde A=",
 Cell[BoxData[
  FormBox[
   RowBox[{"f", "(", 
    SubscriptBox["x", "0"], ")"}], TraditionalForm]]],
 ",  m = f\[CloseCurlyQuote](x)  y X =",
 Cell[BoxData[
  FormBox[
   RowBox[{" ", 
    RowBox[{"(", 
     RowBox[{"x", "-", 
      SubscriptBox["x", "0"]}], ")"}]}], TraditionalForm]]],
 " "
}], "MathCaption",
 CellChangeTimes->{{3.484033695921688*^9, 3.484033774944208*^9}, {
   3.4840340398563604`*^9, 3.4840340972956457`*^9}, {3.496578534857711*^9, 
   3.496578535918513*^9}, {3.524554076894932*^9, 3.5245541167218018`*^9}, {
   3.5245541485770574`*^9, 3.5245541499186597`*^9}, {3.524638208444361*^9, 
   3.5246382538872414`*^9}, {3.5272458783836346`*^9, 
   3.5272458794756365`*^9}, {3.5445164606431875`*^9, 
   3.5445164981924534`*^9}, {3.561015185054055*^9, 3.5610152376571164`*^9}, 
   3.561015295781138*^9, {3.5612114730382166`*^9, 3.5612115142587614`*^9}, {
   3.561211556298868*^9, 3.5612115838570356`*^9}, {3.5612118812864437`*^9, 
   3.561211915859999*^9}, {3.561212924490428*^9, 3.561212974488748*^9}, {
   3.5612130125938406`*^9, 3.5612131833932824`*^9}, 3.5619822827770247`*^9, {
   3.5619823137266054`*^9, 3.5619823247833786`*^9}, 3.5619826687038574`*^9, {
   3.562045632405878*^9, 3.5620457706755877`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Manipulate", "[", "\[IndentingNewLine]", 
  RowBox[{
   RowBox[{
    RowBox[{"If", "[", 
     RowBox[{
      RowBox[{
       RowBox[{"fcn", "===", "Log"}], "&&", 
       RowBox[{"a", "<", ".001"}]}], ",", 
      RowBox[{"a", "=", ".001"}]}], "]"}], ";", "\[IndentingNewLine]", 
    RowBox[{"(*", 
     RowBox[{
     "set", " ", "height", " ", "of", " ", "inset", " ", "text", " ", "for", 
      " ", "slope"}], "*)"}], "\[IndentingNewLine]", 
    RowBox[{"m", "=", 
     RowBox[{"Max", "[", 
      RowBox[{
       RowBox[{"Abs", "[", 
        RowBox[{"fcn", "[", "5", "]"}], "]"}], ",", 
       RowBox[{"Abs", "[", 
        RowBox[{"fcn", "[", "6", "]"}], "]"}]}], "]"}]}], ";", 
    "\[IndentingNewLine]", 
    RowBox[{"(*", 
     RowBox[{"change", " ", "domain", " ", "for", " ", "log"}], "*)"}], 
    "\[IndentingNewLine]", 
    RowBox[{"If", "[", 
     RowBox[{
      RowBox[{
       RowBox[{"fcn", "[", "2", "]"}], "\[Equal]", 
       RowBox[{"Log", "[", "2", "]"}]}], ",", 
      RowBox[{"left", "=", ".001"}], ",", 
      RowBox[{"left", "=", 
       RowBox[{"-", "8"}]}]}], "]"}], ";", "\[IndentingNewLine]", 
    RowBox[{"(*", 
     RowBox[{
     "change", " ", "plotrange", " ", "for", " ", "log", " ", "and", " ", 
      "trig", " ", "functions"}], "*)"}], "\[IndentingNewLine]", 
    RowBox[{"Which", "[", 
     RowBox[{
      RowBox[{
       RowBox[{"fcn", "[", "2", "]"}], "\[Equal]", 
       RowBox[{"Log", "[", "2", "]"}]}], ",", 
      RowBox[{"r", "=", 
       RowBox[{"{", 
        RowBox[{
         RowBox[{"-", "2"}], ",", "3"}], "}"}]}], ",", 
      RowBox[{
       RowBox[{"fcn", "[", 
        RowBox[{"Pi", "/", "4"}], "]"}], "==", 
       RowBox[{"Sin", "[", 
        RowBox[{"Pi", "/", "4"}], "]"}]}], ",", 
      RowBox[{"r", "=", 
       RowBox[{"{", 
        RowBox[{
         RowBox[{"-", "2"}], ",", "2"}], "}"}]}], ",", "True", ",", 
      RowBox[{"r", "=", "Automatic"}]}], "]"}], ";", "\[IndentingNewLine]", 
    "\[IndentingNewLine]", 
    RowBox[{"GraphicsRow", "[", "\[IndentingNewLine]", "\[IndentingNewLine]", 
     RowBox[{"(*", 
      RowBox[{
       RowBox[{"first", " ", "row"}], " ", "-", " ", "function"}], "*)"}], 
     RowBox[{
      RowBox[{"{", 
       RowBox[{
        RowBox[{"Show", "[", 
         RowBox[{
          RowBox[{"Plot", "[", 
           RowBox[{
            RowBox[{"fcn", "[", "x", "]"}], ",", 
            RowBox[{"{", 
             RowBox[{"x", ",", "left", ",", "8"}], "}"}], ",", 
            RowBox[{"PlotStyle", "\[Rule]", 
             RowBox[{"Thickness", "[", ".007", "]"}]}], ",", 
            RowBox[{"ImageSize", "\[Rule]", 
             RowBox[{"Scaled", "[", ".7", "]"}]}], ",", 
            RowBox[{"PlotRange", "\[Rule]", 
             RowBox[{"{", 
              RowBox[{
               RowBox[{"{", 
                RowBox[{
                 RowBox[{"-", "8"}], ",", "12"}], "}"}], ",", "r"}], "}"}]}], 
            ",", 
            RowBox[{"PlotLabel", " ", "\[Rule]", 
             RowBox[{"Style", "[", 
              RowBox[{
               RowBox[{"Framed", "[", 
                RowBox[{
                 RowBox[{"Row", "[", 
                  RowBox[{"{", 
                   RowBox[{"\"\<funci\[OAcute]n \>\"", ",", 
                    RowBox[{"Style", "[", 
                    RowBox[{"\"\<f\>\"", ",", "Italic"}], "]"}], ",", 
                    "\"\<(\>\"", ",", 
                    RowBox[{"Style", "[", 
                    RowBox[{"\"\<x\>\"", ",", "Italic"}], "]"}], ",", 
                    "\"\<)\>\"", ",", "\"\< = \>\"", ",", 
                    RowBox[{"ToString", "[", 
                    RowBox[{
                    StyleBox[
                    RowBox[{"fcn", "[", "x", "]"}], "WarholOrange"], ",", 
                    "TraditionalForm"}], 
                    StyleBox["]", "WarholOrange"]}]}], "}"}], "]"}], ",", 
                 RowBox[{"Background", "\[Rule]", "LightGray"}]}], "]"}], ",",
                "14"}], "]"}]}], ",", 
            RowBox[{"Epilog", "\[Rule]", " ", 
             RowBox[{"Inset", "[", 
              RowBox[{
               RowBox[{"Style", "[", 
                RowBox[{
                 RowBox[{"Row", "[", 
                  RowBox[{"{", 
                   RowBox[{
                    RowBox[{"Style", "[", 
                    RowBox[{"\"\<m\>\"", ",", " ", "Italic"}], "]"}], ",", 
                    "\"\< = \>\"", ",", 
                    RowBox[{"NumberForm", "[", 
                    RowBox[{
                    RowBox[{"N", "[", 
                    RowBox[{
                    RowBox[{"fcn", "'"}], "[", "a", "]"}], "]"}], ",", 
                    RowBox[{"{", 
                    RowBox[{"4", ",", "2"}], "}"}]}], "]"}]}], "}"}], "]"}], 
                 ",", "14", ",", 
                 RowBox[{"Background", "\[Rule]", "LightRed"}]}], "]"}], ",", 
               RowBox[{"{", 
                RowBox[{"10", ",", 
                 RowBox[{"m", "/", "2"}]}], "}"}]}], "]"}]}]}], "]"}], ",", 
          "\[IndentingNewLine]", 
          RowBox[{"ListPlot", "[", 
           RowBox[{
            RowBox[{"{", 
             RowBox[{"{", 
              RowBox[{"a", ",", 
               RowBox[{"fcn", "[", "a", "]"}]}], "}"}], "}"}], ",", 
            RowBox[{"PlotStyle", "\[Rule]", 
             RowBox[{"{", 
              RowBox[{"Black", ",", 
               RowBox[{"PointSize", "[", "Large", "]"}]}], "}"}]}]}], "]"}], 
          ",", "\[IndentingNewLine]", 
          RowBox[{"Plot", "[", 
           RowBox[{
            RowBox[{
             RowBox[{"fcn", "[", "a", "]"}], "+", 
             RowBox[{
              RowBox[{
               RowBox[{"fcn", "'"}], "[", "a", "]"}], "*", 
              RowBox[{"(", 
               RowBox[{"x", "-", "a"}], ")"}]}]}], ",", 
            RowBox[{"{", 
             RowBox[{"x", ",", 
              RowBox[{"a", "-", "2"}], ",", 
              RowBox[{"a", "+", "2"}]}], "}"}], ",", "\[IndentingNewLine]", 
            RowBox[{"PlotStyle", "\[Rule]", 
             RowBox[{"{", 
              RowBox[{"Red", ",", 
               RowBox[{"Thickness", "[", ".012", "]"}], ",", 
               RowBox[{"Opacity", "[", ".6", "]"}]}], "}"}]}]}], "]"}], ",", 
          RowBox[{"PlotRangePadding", "\[Rule]", "1"}]}], "]"}], ",", 
        "\[IndentingNewLine]", "\[IndentingNewLine]", 
        RowBox[{"(*", 
         RowBox[{
          RowBox[{"second", " ", "row"}], " ", "-", " ", "derivative"}], 
         "*)"}], "\[IndentingNewLine]", 
        RowBox[{"Show", "[", "\[IndentingNewLine]", 
         RowBox[{
          RowBox[{"Plot", "[", 
           RowBox[{
            RowBox[{
             RowBox[{"fcn", "'"}], "[", "x", "]"}], ",", 
            RowBox[{"{", 
             RowBox[{"x", ",", "left", ",", "8"}], "}"}], ",", 
            RowBox[{"PlotStyle", "\[Rule]", 
             RowBox[{"Thickness", "[", ".007", "]"}]}], " ", ",", 
            RowBox[{"ImageSize", "\[Rule]", 
             RowBox[{"Scaled", "[", ".7", "]"}]}], ",", 
            RowBox[{"PlotRange", "\[Rule]", 
             RowBox[{"{", 
              RowBox[{
               RowBox[{"{", 
                RowBox[{
                 RowBox[{"-", "8"}], ",", "12"}], "}"}], ",", "r"}], "}"}]}], 
            ",", 
            RowBox[{"PlotLabel", " ", "\[Rule]", 
             RowBox[{"Style", "[", 
              RowBox[{
               RowBox[{"Framed", "[", 
                RowBox[{
                 RowBox[{"Row", "[", 
                  RowBox[{"{", 
                   RowBox[{"\"\<derivada \>\"", ",", 
                    RowBox[{"Style", "[", 
                    RowBox[{"\"\<f'\>\"", ",", "Italic"}], "]"}], ",", 
                    "\"\<(\>\"", ",", 
                    RowBox[{"Style", "[", 
                    RowBox[{"\"\<x\>\"", ",", "Italic"}], "]"}], ",", 
                    "\"\<)\>\""}], "}"}], "]"}], ",", 
                 RowBox[{"Background", "\[Rule]", "LightGray"}]}], "]"}], ",",
                "14"}], "]"}]}], ",", 
            RowBox[{"Epilog", "\[Rule]", " ", 
             RowBox[{"Inset", "[", 
              RowBox[{
               RowBox[{"Style", "[", 
                RowBox[{
                 RowBox[{"Row", "[", 
                  RowBox[{"{", 
                   RowBox[{
                    RowBox[{"Style", "[", 
                    RowBox[{"\"\<y\>\"", ",", " ", "Italic"}], "]"}], ",", 
                    "\"\< = \>\"", ",", 
                    RowBox[{"NumberForm", "[", 
                    RowBox[{
                    RowBox[{"N", "[", 
                    RowBox[{
                    RowBox[{"fcn", "'"}], "[", "a", "]"}], "]"}], ",", 
                    RowBox[{"{", 
                    RowBox[{"4", ",", "2"}], "}"}]}], "]"}]}], "}"}], "]"}], 
                 ",", "14", ",", 
                 RowBox[{"Background", "\[Rule]", "LightRed"}]}], "]"}], ",", 
               RowBox[{"{", 
                RowBox[{"10", ",", 
                 RowBox[{
                  RowBox[{"fcn", "'"}], "[", "a", "]"}]}], "}"}]}], "]"}]}]}],
            "]"}], ",", "\[IndentingNewLine]", 
          RowBox[{"Graphics", "[", 
           RowBox[{"{", 
            RowBox[{"Dashed", ",", "Red", ",", 
             RowBox[{"Line", "[", 
              RowBox[{"{", 
               RowBox[{
                RowBox[{"{", 
                 RowBox[{"0", ",", 
                  RowBox[{
                   RowBox[{"fcn", "'"}], "[", "a", "]"}]}], "}"}], ",", 
                RowBox[{"{", 
                 RowBox[{"a", ",", 
                  RowBox[{
                   RowBox[{"fcn", "'"}], "[", "a", "]"}]}], "}"}]}], "}"}], 
              "]"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", 
          RowBox[{"ListPlot", "[", 
           RowBox[{
            RowBox[{"{", 
             RowBox[{"{", 
              RowBox[{"a", ",", 
               RowBox[{
                RowBox[{"fcn", "'"}], "[", "a", "]"}]}], "}"}], "}"}], ",", 
            RowBox[{"PlotStyle", "\[Rule]", 
             RowBox[{"{", 
              RowBox[{
               RowBox[{"PointSize", "[", "Large", "]"}], ",", "Red"}], 
              "}"}]}]}], "]"}], ",", 
          RowBox[{"PlotRangePadding", "\[Rule]", "1"}]}], "]"}]}], "}"}], ",", 
      RowBox[{"ImageSize", "\[Rule]", 
       RowBox[{"{", 
        RowBox[{"600", ",", "300"}], "}"}]}]}], "]"}]}], ",", 
   "\[IndentingNewLine]", "\[IndentingNewLine]", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"a", ",", "1", ",", "\"\<x\>\""}], "}"}], ",", 
     RowBox[{"Dynamic", "[", 
      RowBox[{"If", "[", 
       RowBox[{
        RowBox[{"fcn", "===", "Log"}], ",", ".001", ",", 
        RowBox[{"-", "8"}]}], "]"}], "]"}], ",", "8", ",", 
     RowBox[{"Appearance", "\[Rule]", "\"\<Labeled\>\""}]}], "}"}], ",", 
   "\[IndentingNewLine]", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"fcn", ",", 
       RowBox[{
        RowBox[{"(", 
         RowBox[{"#", "^", "2"}], ")"}], "&"}], ",", 
       "\"\<funci\[OAcute]n\>\""}], "}"}], ",", "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"Identity", "\[Rule]", 
        RowBox[{"ToString", "[", 
         RowBox[{"x", ",", "TraditionalForm"}], "]"}]}], ",", 
       "\[IndentingNewLine]", 
       RowBox[{
        RowBox[{"(", 
         RowBox[{
          RowBox[{"(", 
           RowBox[{"#", "^", "2"}], ")"}], "&"}], ")"}], "\[Rule]", 
        RowBox[{"ToString", "[", 
         RowBox[{
          RowBox[{"x", "^", "2"}], ",", "TraditionalForm"}], "]"}]}], ",", 
       "\[IndentingNewLine]", 
       RowBox[{
        RowBox[{"(", 
         RowBox[{
          RowBox[{"(", 
           RowBox[{"#", "^", "3"}], ")"}], "&"}], ")"}], "\[Rule]", 
        RowBox[{"ToString", "[", 
         RowBox[{
          RowBox[{"x", "^", "3"}], ",", "TraditionalForm"}], "]"}]}], ",", 
       "\[IndentingNewLine]", 
       RowBox[{"Sin", "\[Rule]", 
        RowBox[{"ToString", "[", 
         RowBox[{
          RowBox[{"Sin", "[", "x", "]"}], ",", "TraditionalForm"}], "]"}]}], 
       ",", "\[IndentingNewLine]", 
       RowBox[{"Cos", "\[Rule]", 
        RowBox[{"ToString", "[", 
         RowBox[{
          RowBox[{"Cos", "[", "x", "]"}], ",", "TraditionalForm"}], "]"}]}], 
       ",", "\[IndentingNewLine]", 
       RowBox[{"Exp", "\[Rule]", 
        RowBox[{"ToString", "[", 
         RowBox[{
          RowBox[{"Exp", "[", "x", "]"}], ",", "TraditionalForm"}], "]"}]}], 
       ",", "\[IndentingNewLine]", 
       RowBox[{"Log", "\[Rule]", " ", 
        RowBox[{"ToString", "[", 
         RowBox[{
          RowBox[{"Log", "[", "x", "]"}], ",", "TraditionalForm"}], "]"}]}]}],
       "}"}], ",", "\[IndentingNewLine]", 
     RowBox[{"ControlType", "\[Rule]", "SetterBar"}]}], "}"}], ",", 
   RowBox[{"TrackedSymbols", "\[Rule]", "Manipulate"}]}], "]"}]], "Input",
 CellChangeTimes->{
  3.35696210375764*^9, 3.4335128909306393`*^9, {3.433513000593799*^9, 
   3.433513001837318*^9}, {3.4335213265068927`*^9, 3.433521369234165*^9}, {
   3.4335214008913307`*^9, 3.4335214090251436`*^9}, {3.433596481726352*^9, 
   3.433596484997679*^9}, {3.4336944999703407`*^9, 3.433694570195362*^9}, {
   3.433694624098752*^9, 3.4336946685421963`*^9}, {3.4342142727869854`*^9, 
   3.4342142993596425`*^9}, {3.5612121478098307`*^9, 
   3.5612121628016577`*^9}, {3.561212358452654*^9, 3.5612123618520575`*^9}}],

Cell[BoxData[
 FormBox[
  TagBox[
   FormBox[
    StyleBox[
     DynamicModuleBox[{$CellContext`a$$ = 0, $CellContext`fcn$$ = #^2& , 
      Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, 
      Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ =
       1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{
         Hold[$CellContext`a$$], 1, "x"}, 
        Dynamic[
         If[$CellContext`fcn$$ === Log, 0.001, -8]], 8}, {{
         Hold[$CellContext`fcn$$], #^2& , "funci\[OAcute]n"}, {
        Identity -> "\!\(TraditionalForm\`x\)", (#^2& ) -> 
         "\!\(TraditionalForm\`x\^2\)", (#^3& ) -> 
         "\!\(TraditionalForm\`x\^3\)", Sin -> 
         "\!\(TraditionalForm\`\(sin(x)\)\)", Cos -> 
         "\!\(TraditionalForm\`\(cos(x)\)\)", Exp -> 
         "\!\(TraditionalForm\`\[ExponentialE]\^x\)", Log -> 
         "\!\(TraditionalForm\`\(log(x)\)\)"}}}, Typeset`size$$ = {
      1200., {289., 311.}}, Typeset`update$$ = 0, Typeset`initDone$$, 
      Typeset`skipInitDone$$ = True, $CellContext`a$3209$$ = 
      0, $CellContext`fcn$3210$$ = False}, 
      DynamicBox[Manipulate`ManipulateBoxes[
       1, TraditionalForm, 
        "Variables" :> {$CellContext`a$$ = 1, $CellContext`fcn$$ = #^2& }, 
        "ControllerVariables" :> {
          Hold[$CellContext`a$$, $CellContext`a$3209$$, 0], 
          Hold[$CellContext`fcn$$, $CellContext`fcn$3210$$, False]}, 
        "OtherVariables" :> {
         Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, 
          Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, 
          Typeset`specs$$, Typeset`size$$, Typeset`update$$, 
          Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> (If[
           
           And[$CellContext`fcn$$ === Log, $CellContext`a$$ < 
            0.001], $CellContext`a$$ = 0.001]; $CellContext`m = Max[
            Abs[
             $CellContext`fcn$$[5]], 
            Abs[
             $CellContext`fcn$$[6]]]; 
         If[$CellContext`fcn$$[2] == Log[2], $CellContext`left = 
           0.001, $CellContext`left = -8]; 
         Which[$CellContext`fcn$$[2] == 
           Log[2], $CellContext`r = {-2, 3}, $CellContext`fcn$$[Pi/4] == 
           Sin[Pi/4], $CellContext`r = {-2, 2}, True, $CellContext`r = 
           Automatic]; GraphicsRow[{
            Show[
             Plot[
              $CellContext`fcn$$[$CellContext`x], {$CellContext`x, \
$CellContext`left, 8}, PlotStyle -> Thickness[0.007], ImageSize -> 
              Scaled[0.7], PlotRange -> {{-8, 12}, $CellContext`r}, PlotLabel -> 
              Style[
                Framed[
                 Row[{"funci\[OAcute]n ", 
                   Style["f", Italic], "(", 
                   Style["x", Italic], ")", " = ", 
                   ToString[
                    $CellContext`fcn$$[$CellContext`x], TraditionalForm]}], 
                 Background -> LightGray], 14], Epilog -> Inset[
                Style[
                 Row[{
                   Style["m", Italic], " = ", 
                   NumberForm[
                    N[
                    Derivative[1][$CellContext`fcn$$][$CellContext`a$$]], {4, 
                    2}]}], 14, Background -> LightRed], {
                10, $CellContext`m/2}]], 
             ListPlot[{{$CellContext`a$$, 
                $CellContext`fcn$$[$CellContext`a$$]}}, PlotStyle -> {Black, 
                PointSize[Large]}], 
             
             Plot[$CellContext`fcn$$[$CellContext`a$$] + 
              Derivative[
                1][$CellContext`fcn$$][$CellContext`a$$] ($CellContext`x - \
$CellContext`a$$), {$CellContext`x, $CellContext`a$$ - 2, $CellContext`a$$ + 
               2}, PlotStyle -> {Red, 
                Thickness[0.012], 
                Opacity[0.6]}], PlotRangePadding -> 1], 
            Show[
             Plot[
              Derivative[
              1][$CellContext`fcn$$][$CellContext`x], {$CellContext`x, \
$CellContext`left, 8}, PlotStyle -> Thickness[0.007], ImageSize -> 
              Scaled[0.7], PlotRange -> {{-8, 12}, $CellContext`r}, PlotLabel -> 
              Style[
                Framed[
                 Row[{"derivada ", 
                   Style["f'", Italic], "(", 
                   Style["x", Italic], ")"}], Background -> LightGray], 14], 
              Epilog -> Inset[
                Style[
                 Row[{
                   Style["y", Italic], " = ", 
                   NumberForm[
                    N[
                    Derivative[1][$CellContext`fcn$$][$CellContext`a$$]], {4, 
                    2}]}], 14, Background -> LightRed], {10, 
                 Derivative[1][$CellContext`fcn$$][$CellContext`a$$]}]], 
             Graphics[{Dashed, Red, 
               Line[{{0, 
                  Derivative[
                  1][$CellContext`fcn$$][$CellContext`a$$]}, \
{$CellContext`a$$, 
                  Derivative[1][$CellContext`fcn$$][$CellContext`a$$]}}]}], 
             ListPlot[{{$CellContext`a$$, 
                Derivative[1][$CellContext`fcn$$][$CellContext`a$$]}}, 
              PlotStyle -> {
                PointSize[Large], Red}], PlotRangePadding -> 1]}, 
           ImageSize -> {600, 300}]), 
        "Specifications" :> {{{$CellContext`a$$, 1, "x"}, 
           Dynamic[
            If[$CellContext`fcn$$ === Log, 0.001, -8]], 8, Appearance -> 
           "Labeled"}, {{$CellContext`fcn$$, #^2& , "funci\[OAcute]n"}, {
           Identity -> "\!\(TraditionalForm\`x\)", (#^2& ) -> 
            "\!\(TraditionalForm\`x\^2\)", (#^3& ) -> 
            "\!\(TraditionalForm\`x\^3\)", Sin -> 
            "\!\(TraditionalForm\`\(sin(x)\)\)", Cos -> 
            "\!\(TraditionalForm\`\(cos(x)\)\)", Exp -> 
            "\!\(TraditionalForm\`\[ExponentialE]\^x\)", Log -> 
            "\!\(TraditionalForm\`\(log(x)\)\)"}, ControlType -> SetterBar}}, 
        "Options" :> {TrackedSymbols -> Manipulate}, "DefaultOptions" :> {}],
       ImageSizeCache->{1288., {416., 429.}},
       SingleEvaluation->True],
      Deinitialization:>None,
      DynamicModuleValues:>{},
      SynchronousInitialization->True,
      UnsavedVariables:>{Typeset`initDone$$},
      UntrackedVariables:>{Typeset`size$$}], "Manipulate",
     Deployed->True,
     StripOnInput->False],
    TraditionalForm],
   Manipulate`InterpretManipulate[1]], TraditionalForm]], "Output",
 CellChangeTimes->{3.5612121666487455`*^9, 3.561900632768388*^9}]
}, {2}]],

Cell[TextData[{
 "Adaptado de \[NonBreakingSpace]",
 ButtonBox["http://demonstrations.wolfram.com/DerivativeAsAFunction/",
  BaseStyle->"Hyperlink",
  ButtonData->{
    URL["http://demonstrations.wolfram.com/DerivativeAsAFunction/"], None},
  ButtonNote->"http://demonstrations.wolfram.com/DerivativeAsAFunction/"],
 " por: ",
 ButtonBox["Jim Brandt",
  BaseStyle->"Hyperlink",
  ButtonData->{
    URL["http://demonstrations.wolfram.com/author.html?author=Jim+Brandt"], 
    None},
  ButtonNote->
   "http://demonstrations.wolfram.com/author.html?author=Jim+Brandt"]
}], "Text",
 CellMargins->{{48, Inherited}, {0, Inherited}},
 CellChangeTimes->{{3.5612122730503473`*^9, 3.561212313210881*^9}},
 FontFamily->"Verdana",
 FontSize->9,
 FontColor->GrayLevel[0.5]],

Cell[TextData[{
 "Un enlace intesante: ",
 ButtonBox["http://demonstrations.wolfram.com/\
FiniteDifferenceApproximationsOfTheFirstDerivativeOfAFunctio/",
  BaseStyle->"Hyperlink",
  ButtonData->{
    URL["http://demonstrations.wolfram.com/\
FiniteDifferenceApproximationsOfTheFirstDerivativeOfAFunctio/"], None},
  ButtonNote->
   "http://demonstrations.wolfram.com/\
FiniteDifferenceApproximationsOfTheFirstDerivativeOfAFunctio/"]
}], "Text",
 CellChangeTimes->{{3.561212465961726*^9, 3.561212521642089*^9}}]
}, Closed]],

Cell[CellGroupData[{

Cell["\<\
Teoremas relacionados con la derivaci\[OAcute]n\
\>", "Subsubsection",
 CellChangeTimes->{
  3.562040439605258*^9, {3.562041104093302*^9, 3.5620411132134795`*^9}},
 FontSize->16],

Cell["\<\
Si f una funci\[OAcute]n continua en el intervalo I y derivable en  el \
interior de I (esto es en puntos distintos del inicial y final) entonces: 
\tSi f '(x) > 0  \[ForAll]  x del interior de I entonces f es estrictamente \
creciente en I 
\tSi f '(x) < 0  \[ForAll]  x del interior de I entonces f es estrictamente \
creciente en I \
\>", "Text",
 CellChangeTimes->{
  3.5620411258111277`*^9, {3.562041596742407*^9, 3.5620415998217444`*^9}}],

Cell[TextData[{
 "Si f es continua en a y los l\[IAcute]mites laterales coinciden, esto es: ",
 Cell[BoxData[
  RowBox[{
   StyleBox[
    UnderscriptBox["lim", 
     RowBox[{"x", "\[Rule]", 
      SuperscriptBox["a", "+"]}]],
    FontSize->12], 
   StyleBox["\[ThinSpace]",
    FontSize->12], 
   StyleBox[
    RowBox[{"f", 
     RowBox[{"(", "x", ")"}]}],
    FontSize->12], " "}]],
  CellChangeTimes->{{3.5610525000010576`*^9, 3.5610525071769466`*^9}, 
    3.561052604276122*^9},
  FontSize->18],
 "= ",
 Cell[BoxData[
  StyleBox[
   RowBox[{
    RowBox[{
     UnderscriptBox["lim", 
      RowBox[{"x", "\[Rule]", 
       SuperscriptBox["a", "-"]}]], "\[ThinSpace]", 
     RowBox[{"f", 
      RowBox[{"(", "x", ")"}]}]}], "=", "b"}],
   FontSize->12]],
  CellChangeTimes->{{3.5610525000010576`*^9, 3.5610525071769466`*^9}, 
    3.561052604276122*^9},
  FontSize->18],
 ", entonces f es derivable en a y su valor es b, es decir ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    RowBox[{
     RowBox[{"f", "'"}], 
     RowBox[{"(", "a", ")"}]}], " ", "=", " ", "b"}], TraditionalForm]]],
 "."
}], "Text",
 CellChangeTimes->{
  3.5620411258111277`*^9, {3.56204124223798*^9, 3.5620413016225815`*^9}, {
   3.5620413756210957`*^9, 3.5620415752836027`*^9}}]
}, Closed]]
}, Closed]],

Cell[CellGroupData[{

Cell["\<\
Reglas de la derivaci\[OAcute]n de funciones\
\>", "Section",
 FontSize->16],

Cell[TextData[{
 "Para las reglas de la derivaci\[OAcute]n y las derivadas mas comunes puede \
consular cualquier libro de matematicas de bachiller o ",
 ButtonBox["http://www.unizar.es/aragon_tres/unidad7/u7der/u7derte30.pdf .",
  BaseStyle->"Hyperlink",
  ButtonData->{
    URL["http://www.unizar.es/aragon_tres/unidad7/u7der/u7derte30.pdf"], None},
  ButtonNote->"http://www.unizar.es/aragon_tres/unidad7/u7der/u7derte30.pdf"]
}], "Text",
 CellChangeTimes->{{3.561122126023121*^9, 3.561122173422052*^9}, {
   3.562043388368644*^9, 3.5620434572414646`*^9}, 3.5620444366258335`*^9}],

Cell[CellGroupData[{

Cell["Derivadas simples mas comunes", "Subsubsection",
 CellChangeTimes->{{3.5620438163444233`*^9, 3.5620438309653654`*^9}, {
  3.5620444631382465`*^9, 3.5620444645294046`*^9}},
 FontSize->16],

Cell[BoxData[
 GraphicsBox[
  TagBox[RasterBox[CompressedData["
1:eJzt3QdYU2f7OP6TcdgjIKCCCIiEoQiK21pXXdSFs8VWa3G8dbdqa62Cq+KA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    "], {{0, 378}, {414, 0}}, {0, 255},
    ColorFunction->RGBColor],
   BoxForm`ImageTag["Byte", ColorSpace -> "RGB", Interleaving -> True],
   Selectable->False],
  BaseStyle->"ImageGraphics",
  ImageSize->Automatic,
  ImageSizeRaw->{414, 378},
  PlotRange->{{0, 414}, {0, 378}}]], "Text",
 CellChangeTimes->{3.5619014486160393`*^9}],

Cell["\<\
Observe que las derivadas anteriores se obtienen de la definicion de \
derivada, como se ha mostrado en la secci\[OAcute]n anterior.\
\>", "Text",
 CellChangeTimes->{{3.562043503287402*^9, 3.5620435933038764`*^9}, {
  3.5620436388247175`*^9, 3.562043639448784*^9}}],

Cell["Con Mathematica se claculan directamente:", "Subitem",
 CellChangeTimes->{{3.5620436418710923`*^9, 3.5620436639739676`*^9}, {
  3.562043714856429*^9, 3.562043716032583*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"y", "[", "x_", "]"}], ":=", 
  RowBox[{"k", " ", 
   RowBox[{"f", "[", "x", "]"}]}]}]], "Input",
 CellChangeTimes->{{3.56112203547688*^9, 3.5611220364128933`*^9}, {
   3.561902015567701*^9, 3.5619020252398124`*^9}, 3.562043688957139*^9}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"y", "'"}], "[", "x", "]"}]], "Input",
 CellChangeTimes->{{3.5611222396904936`*^9, 3.561122243871366*^9}}],

Cell[BoxData[
 FormBox[
  RowBox[{"k", " ", 
   RowBox[{
    SuperscriptBox["f", "\[Prime]",
     MultilineFunction->None], "(", "x", ")"}]}], TraditionalForm]], "Output",
 CellChangeTimes->{3.561122244760537*^9}]
}, Open  ]],

Cell[BoxData[
 RowBox[{
  RowBox[{"y", "[", "x_", "]"}], ":=", 
  SuperscriptBox["x", "a"]}]], "Input",
 CellChangeTimes->{
  3.5619849246569815`*^9, {3.5619942995686817`*^9, 3.561994308242504*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"y", "'"}], "[", "x", "]"}]], "Input",
 CellChangeTimes->{{3.5611222572874517`*^9, 3.5611222682075896`*^9}, {
  3.5619943018463397`*^9, 3.5619943049508195`*^9}}],

Cell[BoxData[
 FormBox[
  RowBox[{"a", " ", 
   SuperscriptBox["x", 
    RowBox[{"a", "-", "1"}]]}], TraditionalForm]], "Output",
 CellChangeTimes->{3.5611222738391976`*^9, 3.561984990647047*^9}]
}, Open  ]],

Cell[BoxData[
 RowBox[{
  RowBox[{"y", "[", "x_", "]"}], ":=", 
  RowBox[{"Sin", "[", "x", "]"}]}]], "Input",
 CellChangeTimes->{
  3.5619849246569815`*^9, {3.5619850026139374`*^9, 3.5619850078402386`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"y", "'"}], "[", "x", "]"}]], "Input",
 CellChangeTimes->{{3.5611222572874517`*^9, 3.5611222682075896`*^9}}],

Cell[BoxData[
 FormBox[
  RowBox[{"cos", "(", "x", ")"}], TraditionalForm]], "Output",
 CellChangeTimes->{3.5619850272321577`*^9}]
}, Open  ]],

Cell[BoxData[
 RowBox[{
  RowBox[{"y", "[", "x_", "]"}], ":=", 
  SuperscriptBox["\[ExponentialE]", "x"]}]], "Input",
 CellChangeTimes->{
  3.5619849246569815`*^9, {3.5619850026139374`*^9, 3.5619850078402386`*^9}, {
   3.5619850549705577`*^9, 3.561985064128286*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"y", "'"}], "[", "x", "]"}]], "Input",
 CellChangeTimes->{{3.5611222572874517`*^9, 3.5611222682075896`*^9}}],

Cell[BoxData[
 FormBox[
  SuperscriptBox["\[ExponentialE]", "x"], TraditionalForm]], "Output",
 CellChangeTimes->{3.5619850776542664`*^9}]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell["Suma y resta", "Subsubsection",
 FontSize->16],

Cell[BoxData[
 RowBox[{"Clear", "[", "\"\<Global`*\>\"", "]"}]], "Input"],

Cell[TextData[{
 "Dada una funcion ",
 Cell[BoxData[
  FormBox[
   RowBox[{"y", "(", "x", ")"}], TraditionalForm]]]
}], "Text",
 FontSize->16],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"y", "(", "x_", ")"}], ":=", 
   RowBox[{
    RowBox[{"f", "(", "x", ")"}], "+", 
    RowBox[{"g", "(", "x", ")"}]}]}], TraditionalForm]], "Input"],

Cell["Su derivada es", "Text",
 FontSize->16],

Cell[CellGroupData[{

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    SuperscriptBox["y", "\[Prime]",
     MultilineFunction->None], "(", "x", ")"}], " "}], 
  TraditionalForm]], "Input",
 CellChangeTimes->{3.56112228597611*^9}],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    SuperscriptBox["f", "\[Prime]",
     MultilineFunction->None], "(", "x", ")"}], "+", 
   RowBox[{
    SuperscriptBox["g", "\[Prime]",
     MultilineFunction->None], "(", "x", ")"}]}], TraditionalForm]], "Output",
 CellChangeTimes->{3.5611222896109447`*^9}]
}, Open  ]],

Cell["Para", "Text",
 CellChangeTimes->{{3.5620437778885016`*^9, 3.5620438040888577`*^9}},
 FontSize->16],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"y", "(", "x_", ")"}], ":=", 
   RowBox[{
    RowBox[{"f", "(", "x", ")"}], "-", 
    RowBox[{"g", "(", "x", ")"}]}]}], TraditionalForm]], "Input"],

Cell["Su derivada es", "Text",
 FontSize->16],

Cell[CellGroupData[{

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    SuperscriptBox["y", "\[Prime]",
     MultilineFunction->None], "(", "x", ")"}], " "}], 
  TraditionalForm]], "Input",
 CellChangeTimes->{{3.561122307145537*^9, 3.5611223137131605`*^9}}],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    SuperscriptBox["f", "\[Prime]",
     MultilineFunction->None], "(", "x", ")"}], "-", 
   RowBox[{
    SuperscriptBox["g", "\[Prime]",
     MultilineFunction->None], "(", "x", ")"}]}], TraditionalForm]], "Output",
 CellChangeTimes->{3.5611223203900223`*^9}]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell["Producto", "Subsubsection",
 FontSize->16],

Cell[TextData[{
 "Dada una funci\[OAcute]n ",
 Cell[BoxData[
  FormBox[
   RowBox[{"y", "(", "x", ")"}], TraditionalForm]]]
}], "Text",
 CellChangeTimes->{{3.5612096957761593`*^9, 3.561209715123826*^9}, {
  3.561989091832871*^9, 3.561989092503684*^9}},
 FontSize->16],

Cell[BoxData[
 RowBox[{
  RowBox[{"y", "[", "x_", "]"}], ":=", 
  RowBox[{
   RowBox[{"f", "[", "x", "]"}], " ", 
   RowBox[{"g", "[", "x", "]"}]}]}]], "Input",
 CellChangeTimes->{3.5619890165460987`*^9}],

Cell["Su derivada es", "Text",
 FontSize->16],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"y", "'"}], "[", "x", "]"}]], "Input",
 CellChangeTimes->{{3.561122307145537*^9, 3.5611223137131605`*^9}, 
   3.56198907306571*^9, {3.5619892280702906`*^9, 3.5619892293027143`*^9}, {
   3.5619892653238072`*^9, 3.5619892679446573`*^9}}],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    RowBox[{"g", "(", "x", ")"}], " ", 
    RowBox[{
     SuperscriptBox["f", "\[Prime]",
      MultilineFunction->None], "(", "x", ")"}]}], "+", 
   RowBox[{
    RowBox[{"f", "(", "x", ")"}], " ", 
    RowBox[{
     SuperscriptBox["g", "\[Prime]",
      MultilineFunction->None], "(", "x", ")"}]}]}], 
  TraditionalForm]], "Output",
 CellChangeTimes->{3.561989271220721*^9}]
}, Open  ]],

Cell[TextData[{
 "Ejemplo:  Calcular y\[CloseCurlyQuote](x) de la funci\[OAcute]n y(x)= ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    RowBox[{"(", 
     RowBox[{
      SuperscriptBox["x", "3"], "-", "x"}], ")"}], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"5", " ", 
       SuperscriptBox["x", "4"]}], "+", 
      SuperscriptBox["x", "2"]}], ")"}]}], TraditionalForm]]]
}], "Text",
 CellChangeTimes->{{3.5611223699673023`*^9, 3.561122387533027*^9}, {
  3.5611225316939287`*^9, 3.5611225481520777`*^9}, {3.5612095686076593`*^9, 
  3.561209608216857*^9}},
 FontSize->16],

Cell[BoxData[
 RowBox[{
  RowBox[{"y", "[", "x_", "]"}], ":=", 
  RowBox[{
   RowBox[{"(", 
    RowBox[{
     SuperscriptBox["x", "3"], "-", "x"}], ")"}], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{"5", " ", 
      SuperscriptBox["x", "4"]}], "+", 
     SuperscriptBox["x", "2"]}], ")"}]}]}]], "Input",
 CellChangeTimes->{3.561994437694623*^9}],

Cell[CellGroupData[{

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    SuperscriptBox["y", "\[Prime]",
     MultilineFunction->None], "(", "x", ")"}], " ", "//", "Simplify"}], 
  TraditionalForm]], "Input",
 CellChangeTimes->{{3.561122307145537*^9, 3.5611223137131605`*^9}, {
  3.561989436411804*^9, 3.561989440530257*^9}}],

Cell[BoxData[
 FormBox[
  RowBox[{
   SuperscriptBox["x", "2"], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{"35", " ", 
      SuperscriptBox["x", "4"]}], "-", 
     RowBox[{"20", " ", 
      SuperscriptBox["x", "2"]}], "-", "3"}], ")"}]}], 
  TraditionalForm]], "Output",
 CellChangeTimes->{3.561122359780465*^9, 3.561989444072503*^9}]
}, Open  ]],

Cell["O paso a paso: y(x_):=f(x)g(x)", "Text",
 CellChangeTimes->{{3.5611224157536836`*^9, 3.5611224644417176`*^9}}],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"f", "(", "x_", ")"}], ":=", 
   RowBox[{
    SuperscriptBox["x", "3"], "-", "x"}]}], TraditionalForm]], "Input"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"g", "(", "x_", ")"}], ":=", 
   RowBox[{
    RowBox[{"5", " ", 
     SuperscriptBox["x", "4"]}], "+", 
    SuperscriptBox["x", "2"]}]}], TraditionalForm]], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    SuperscriptBox["f", "\[Prime]",
     MultilineFunction->None], "(", "x", ")"}], " "}], 
  TraditionalForm]], "Input",
 CellChangeTimes->{3.561122398655965*^9}],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"3", " ", 
    SuperscriptBox["x", "2"]}], "-", "1"}], TraditionalForm]], "Output",
 CellChangeTimes->{3.561122429637806*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    SuperscriptBox["g", "\[Prime]",
     MultilineFunction->None], "(", "x", ")"}], " "}], 
  TraditionalForm]], "Input",
 CellChangeTimes->{3.5611224017915564`*^9}],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"20", " ", 
    SuperscriptBox["x", "3"]}], "+", 
   RowBox[{"2", " ", "x"}]}], TraditionalForm]], "Output",
 CellChangeTimes->{3.5611224296846027`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    SuperscriptBox["y", "\[Prime]",
     MultilineFunction->None], "(", "x", ")"}], " "}], 
  TraditionalForm]], "Input",
 CellChangeTimes->{3.561122404849221*^9}],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    RowBox[{"(", 
     RowBox[{
      SuperscriptBox["x", "3"], "-", "x"}], ")"}], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"20", " ", 
       SuperscriptBox["x", "3"]}], "+", 
      RowBox[{"2", " ", "x"}]}], ")"}]}], "+", 
   RowBox[{
    RowBox[{"(", 
     RowBox[{
      RowBox[{"3", " ", 
       SuperscriptBox["x", "2"]}], "-", "1"}], ")"}], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"5", " ", 
       SuperscriptBox["x", "4"]}], "+", 
      SuperscriptBox["x", "2"]}], ")"}]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{3.5611224297470074`*^9}]
}, Open  ]],

Cell[TextData[{
 "Tambien puede hacerse desarrollando primero ",
 Cell[BoxData[
  FormBox[
   RowBox[{"y", "(", "x", ")"}], TraditionalForm]]]
}], "Text",
 FontSize->16],

Cell[BoxData[
 RowBox[{
  RowBox[{"y", "[", "x_", "]"}], ":=", 
  RowBox[{
   RowBox[{"5", " ", 
    SuperscriptBox["x", "7"]}], "-", 
   RowBox[{"4", " ", 
    SuperscriptBox["x", "5"]}], "-", 
   SuperscriptBox["x", "3"]}]}]], "Input",
 CellChangeTimes->{{3.5619895470650234`*^9, 3.561989564958452*^9}}],

Cell["y derivando", "Text",
 FontSize->16],

Cell[CellGroupData[{

Cell[BoxData[
 FormBox[
  RowBox[{
   SuperscriptBox["y", "\[Prime]",
    MultilineFunction->None], "(", "x", ")"}], TraditionalForm]], "Input",
 CellChangeTimes->{3.5611224768907056`*^9}],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"35", " ", 
    SuperscriptBox["x", "6"]}], "-", 
   RowBox[{"20", " ", 
    SuperscriptBox["x", "4"]}], "-", 
   RowBox[{"3", " ", 
    SuperscriptBox["x", "2"]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{
  3.561122484877906*^9, {3.5619895276739745`*^9, 3.5619895681564937`*^9}}]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell["Divisi\[OAcute]n", "Subsubsection",
 FontSize->16],

Cell[BoxData[
 RowBox[{"Clear", "[", "\"\<Global`*\>\"", "]"}]], "Input"],

Cell["Dada una funcion: ", "Text",
 CellChangeTimes->{{3.562044336216982*^9, 3.5620443379132195`*^9}},
 FontSize->16],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"y", "(", "x_", ")"}], ":=", 
   FractionBox[
    RowBox[{"f", "(", "x", ")"}], 
    RowBox[{"g", "(", "x", ")"}]]}], TraditionalForm]], "Input"],

Cell["Su derivada es", "Text",
 FontSize->16],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    SuperscriptBox["y", "\[Prime]",
     MultilineFunction->None], "(", "x", ")"}], " ", "=", 
   RowBox[{
    RowBox[{
     FractionBox[
      RowBox[{
       RowBox[{
        SuperscriptBox["f", "\[Prime]",
         MultilineFunction->None], "(", "x", ")"}], 
       RowBox[{"g", "(", "x", ")"}]}], 
      SuperscriptBox[
       RowBox[{"g", "(", "x", ")"}], "2"]], "-", 
     FractionBox[
      RowBox[{
       RowBox[{"f", "(", "x", ")"}], " ", 
       RowBox[{
        SuperscriptBox["g", "\[Prime]",
         MultilineFunction->None], "(", "x", ")"}]}], 
      SuperscriptBox[
       RowBox[{"g", "(", "x", ")"}], "2"]]}], "=", 
    FractionBox[
     RowBox[{
      RowBox[{
       RowBox[{
        SuperscriptBox["f", "\[Prime]",
         MultilineFunction->None], "(", "x", ")"}], 
       RowBox[{"g", "(", "x", ")"}]}], "-", 
      RowBox[{
       RowBox[{"f", "(", "x", ")"}], " ", 
       RowBox[{
        SuperscriptBox["g", "\[Prime]",
         MultilineFunction->None], "(", "x", ")"}]}]}], 
     SuperscriptBox[
      RowBox[{"g", "(", "x", ")"}], "2"]]}]}], TraditionalForm]], "Text",
 CellChangeTimes->{{3.5611225818015995`*^9, 3.561122652080221*^9}, {
  3.561989582851882*^9, 3.5619895839438963`*^9}, {3.5619896361577654`*^9, 
  3.5619896510559564`*^9}}],

Cell["Ejemplo", "Text",
 CellChangeTimes->{{3.561209737332026*^9, 3.56120975760947*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"y", "[", "x_", "]"}], ":=", 
  FractionBox[
   RowBox[{
    SuperscriptBox["x", "3"], "-", "x"}], 
   RowBox[{
    RowBox[{"5", " ", 
     SuperscriptBox["x", "4"]}], "+", 
    SuperscriptBox["x", "2"]}]]}]], "Input",
 CellChangeTimes->{3.561985633844781*^9}],

Cell["Se puede derivar directamente ", "Text",
 CellChangeTimes->{{3.5619857027508645`*^9, 3.561985712422989*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"y", "'"}], "[", "x", "]"}], "//", "Simplify"}]], "Input",
 CellChangeTimes->{{3.5619856459973373`*^9, 3.5619856606303244`*^9}}],

Cell[BoxData[
 FormBox[
  FractionBox[
   RowBox[{
    RowBox[{"-", 
     RowBox[{"5", " ", 
      SuperscriptBox["x", "4"]}]}], "+", 
    RowBox[{"16", " ", 
     SuperscriptBox["x", "2"]}], "+", "1"}], 
   SuperscriptBox[
    RowBox[{"(", 
     RowBox[{
      RowBox[{"5", " ", 
       SuperscriptBox["x", "3"]}], "+", "x"}], ")"}], "2"]], 
  TraditionalForm]], "Output",
 CellChangeTimes->{{3.561985650692997*^9, 3.561985661285533*^9}}]
}, Open  ]],

Cell["O, con un fin didactico, paso a paso: ", "Text",
 CellChangeTimes->{{3.5619857157458315`*^9, 3.5619857639192486`*^9}}],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"f", "(", "x_", ")"}], ":=", 
   RowBox[{
    SuperscriptBox["x", "3"], "-", "x"}]}], TraditionalForm]], "Input"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"g", "(", "x_", ")"}], ":=", 
   RowBox[{
    RowBox[{"5", " ", 
     SuperscriptBox["x", "4"]}], "+", 
    SuperscriptBox["x", "2"]}]}], TraditionalForm]], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
 FormBox[
  RowBox[{
   SuperscriptBox["f", "\[Prime]",
    MultilineFunction->None], "(", "x", ")"}], TraditionalForm]], "Input"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"3", " ", 
    SuperscriptBox["x", "2"]}], "-", "1"}], TraditionalForm]], "Output",
 CellChangeTimes->{{3.5612097938139453`*^9, 3.5612098177465563`*^9}, 
   3.5612100096811824`*^9},
 FontSize->16]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 FormBox[
  RowBox[{
   SuperscriptBox["g", "\[Prime]",
    MultilineFunction->None], "(", "x", ")"}], TraditionalForm]], "Input"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"20", " ", 
    SuperscriptBox["x", "3"]}], "+", 
   RowBox[{"2", " ", "x"}]}], TraditionalForm]], "Output",
 CellChangeTimes->{{3.5612097938763423`*^9, 3.5612098177933383`*^9}, 
   3.5612100097279525`*^9},
 FontSize->16]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  FractionBox[
   RowBox[{
    RowBox[{
     RowBox[{
      RowBox[{"f", "'"}], "[", "x", "]"}], " ", 
     RowBox[{"g", "[", "x", "]"}]}], "-", 
    RowBox[{
     RowBox[{"f", "[", "x", "]"}], " ", 
     RowBox[{
      RowBox[{"g", "'"}], "[", "x", "]"}]}]}], 
   SuperscriptBox[
    RowBox[{"g", "[", "x", "]"}], "2"]], "//", "Simplify"}]], "Input",
 CellChangeTimes->{{3.561209875539497*^9, 3.5612099393961906`*^9}, {
  3.561209969690643*^9, 3.5612099999096746`*^9}, {3.5612100484415936`*^9, 
  3.561210061860564*^9}, {3.5612100926667624`*^9, 3.5612101659447765`*^9}}],

Cell[BoxData[
 FormBox[
  FractionBox[
   RowBox[{
    RowBox[{"-", 
     RowBox[{"5", " ", 
      SuperscriptBox["x", "4"]}]}], "+", 
    RowBox[{"16", " ", 
     SuperscriptBox["x", "2"]}], "+", "1"}], 
   SuperscriptBox[
    RowBox[{"(", 
     RowBox[{
      RowBox[{"5", " ", 
       SuperscriptBox["x", "3"]}], "+", "x"}], ")"}], "2"]], 
  TraditionalForm]], "Output",
 CellChangeTimes->{
  3.561209943834815*^9, 3.561210009868354*^9, 3.5612100625937037`*^9, 
   3.5612100966159163`*^9, {3.5612101466348*^9, 3.561210166620638*^9}}]
}, Open  ]],

Cell["O  directamente", "Text",
 CellChangeTimes->{{3.5612101882840624`*^9, 3.56121020253291*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    SuperscriptBox["y", "\[Prime]",
     MultilineFunction->None], "(", "x", ")"}], " ", "//", "Simplify"}], 
  TraditionalForm]], "Input",
 CellChangeTimes->{{3.5612097792577744`*^9, 3.5612098476799645`*^9}}],

Cell[BoxData[
 FormBox[
  FractionBox[
   RowBox[{
    RowBox[{"-", 
     RowBox[{"5", " ", 
      SuperscriptBox["x", "4"]}]}], "+", 
    RowBox[{"16", " ", 
     SuperscriptBox["x", "2"]}], "+", "1"}], 
   SuperscriptBox[
    RowBox[{"(", 
     RowBox[{
      RowBox[{"5", " ", 
       SuperscriptBox["x", "3"]}], "+", "x"}], ")"}], "2"]], 
  TraditionalForm]], "Output",
 CellChangeTimes->{{3.5612097940010943`*^9, 3.5612098486471715`*^9}, 
   3.561210009790349*^9}]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell["Funcion de funci\[OAcute]n", "Subsubsection",
 FontSize->16],

Cell[BoxData[
 RowBox[{"Clear", "[", "\"\<Global`*\>\"", "]"}]], "Input"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"y", "(", "x_", ")"}], ":=", 
   SuperscriptBox[
    RowBox[{"g", "(", "x", ")"}], "a"]}], TraditionalForm]], "Input"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    SuperscriptBox["y", "\[Prime]",
     MultilineFunction->None], "(", "x", ")"}], "=", 
   RowBox[{"a", " ", 
    SuperscriptBox[
     RowBox[{"g", "(", "x", ")"}], 
     RowBox[{"a", "-", "1"}]], " ", 
    RowBox[{
     SuperscriptBox["g", "\[Prime]",
      MultilineFunction->None], "(", "x", ")"}]}]}], 
  TraditionalForm]], "Input"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"y", "(", "x_", ")"}], ":=", 
   RadicalBox[
    RowBox[{
     SuperscriptBox["x", "2"], "+", "1"}], "3"]}], TraditionalForm]], "Text",
 FontSize->16],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"y", "(", "x_", ")"}], ":=", 
   RadicalBox[
    RowBox[{
     SuperscriptBox["x", "2"], "+", "1"}], "3"]}], TraditionalForm]], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
 FormBox[
  RowBox[{
   SuperscriptBox["y", "\[Prime]",
    MultilineFunction->None], "(", "x", ")"}], TraditionalForm]], "Input"],

Cell[BoxData[
 FormBox[
  FractionBox[
   RowBox[{"2", " ", "x"}], 
   RowBox[{"3", " ", 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{
       SuperscriptBox["x", "2"], "+", "1"}], ")"}], 
     RowBox[{"2", "/", "3"}]]}]], TraditionalForm]], "Output",
 FontSize->16]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell["Derivadas logaritmicas  ", "Subsubsection",
 FontSize->16],

Cell[BoxData[
 RowBox[{"y", "=", 
  RowBox[{"A", " ", 
   FractionBox[
    RowBox[{
     SuperscriptBox["x", "p"], 
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{
        RowBox[{"a", " ", "x"}], " ", "+", " ", "b"}], ")"}], "q"]}], 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{
       RowBox[{"c", " ", "x"}], " ", "+", "d"}], ")"}], "r"]]}]}]], "Text",
 FontSize->16],

Cell["Tomando logaritmos se obtiene", "Text",
 FontSize->16],

Cell["ln y = A+p ln(x)+q ln(b+a x)-r ln(d+c x)", "Text",
 FontSize->16],

Cell[BoxData[
 RowBox[{
  FractionBox[
   RowBox[{"y", "'"}], "y"], "=", 
  RowBox[{
   FractionBox["p", "x"], "+", 
   FractionBox[
    RowBox[{"a", " ", "q"}], 
    RowBox[{"b", "+", 
     RowBox[{"a", " ", "x"}]}]], "-", 
   FractionBox[
    RowBox[{"c", " ", "r"}], 
    RowBox[{"d", "+", 
     RowBox[{"c", " ", "x"}]}]]}]}]], "Text",
 FontSize->16],

Cell[BoxData[
 RowBox[{
  RowBox[{"y", "'"}], "=", 
  RowBox[{"A", " ", 
   FractionBox[
    RowBox[{
     SuperscriptBox["x", "p"], 
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{
        RowBox[{"a", " ", "x"}], " ", "+", " ", "b"}], ")"}], "q"]}], 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{
       RowBox[{"c", " ", "x"}], " ", "+", "d"}], ")"}], "r"]], 
   RowBox[{"(", 
    RowBox[{
     FractionBox["p", "x"], "+", 
     FractionBox[
      RowBox[{"a", " ", "q"}], 
      RowBox[{"b", "+", 
       RowBox[{"a", " ", "x"}]}]], "-", 
     FractionBox[
      RowBox[{"c", " ", "r"}], 
      RowBox[{"d", "+", 
       RowBox[{"c", " ", "x"}]}]]}], ")"}]}]}]], "Text",
 FontSize->16]
}, Closed]],

Cell[CellGroupData[{

Cell["\<\
Derivaci\[OAcute]n logar\[IAcute]tmica, ampliaci\[OAcute]n\
\>", "Subsubsection",
 CellChangeTimes->{{3.56121345168908*^9, 3.561213452272145*^9}},
 FontSize->16],

Cell["Hallar la derivada de ", "Text",
 FontSize->16],

Cell[BoxData[
 RowBox[{"y", " ", "=", " ", 
  RowBox[{"A", " ", 
   SuperscriptBox[
    RowBox[{"x", " "}], "p"], 
   FractionBox[
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{
       RowBox[{"a", " ", "x"}], " ", "+", " ", "b"}], ")"}], "q"], 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{
       RowBox[{"c", " ", "x"}], " ", "+", " ", "d"}], ")"}], 
     "r"]]}]}]], "Text",
 FontSize->16],

Cell["\<\
En casos donde aparecen potencias, raices cocientes y combinaciones de ellas \
suele ser util utilizar la derivaci\[OAcute]n logar\[IAcute]tmica. En esta \
caso\
\>", "Text",
 FontSize->16],

Cell[BoxData[
 RowBox[{
  RowBox[{"ln", " ", "y"}], " ", "=", " ", 
  RowBox[{
   RowBox[{"ln", " ", "A"}], "+", " ", 
   RowBox[{"p", " ", "ln", " ", "x"}], " ", "+", 
   RowBox[{"q", " ", "ln", " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"a", " ", "x"}], " ", "+", " ", "b"}], ")"}]}], "-", " ", 
   RowBox[{"r", " ", "ln", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"c", " ", "x"}], " ", "+", " ", "d"}], ")"}]}]}]}]], "Text",
 FontSize->16],

Cell["Lo derivamos respecto a x ", "Text",
 FontSize->16],

Cell[BoxData[
 RowBox[{
  FractionBox[
   RowBox[{"y", "'"}], "y"], " ", "=", "  ", 
  RowBox[{
   FractionBox["p", "x"], " ", "+", 
   RowBox[{"a", 
    FractionBox["q", 
     RowBox[{
      RowBox[{"a", " ", "x"}], " ", "+", " ", "b"}]]}], " ", "-", " ", 
   RowBox[{"c", " ", 
    FractionBox["r", 
     RowBox[{
      RowBox[{"c", " ", "x"}], " ", "+", " ", "d"}]]}]}]}]], "Text",
 FontSize->16],

Cell["Despejamos y, sustituyendola por su valor", "Text",
 FontSize->16],

Cell[BoxData[
 RowBox[{
  RowBox[{"y", "'"}], " ", "=", "   ", 
  RowBox[{"A", " ", 
   SuperscriptBox[
    RowBox[{"x", " "}], "p"], 
   FractionBox[
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{
       RowBox[{"a", " ", "x"}], " ", "+", " ", "b"}], ")"}], "q"], 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{
       RowBox[{"c", " ", "x"}], " ", "+", " ", "d"}], ")"}], "r"]], 
   RowBox[{"(", 
    RowBox[{
     FractionBox["p", "x"], " ", "+", 
     RowBox[{"a", 
      FractionBox["q", 
       RowBox[{
        RowBox[{"a", " ", "x"}], " ", "+", " ", "b"}]]}], " ", "-", " ", 
     RowBox[{"c", " ", 
      FractionBox["r", 
       RowBox[{
        RowBox[{"c", " ", "x"}], " ", "+", " ", "d"}]]}]}], ")"}]}]}]], "Text",
 FontSize->16]
}, Closed]],

Cell[CellGroupData[{

Cell["Funciones compuestas: y(x) = f(u(x))", "Subsubsection",
 FontSize->16],

Cell[BoxData[
 RowBox[{"Clear", "[", "\"\<Global`*\>\"", "]"}]], "Input"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"y", "(", "x_", ")"}], ":=", " ", 
   RowBox[{"f", "(", 
    RowBox[{"u", "(", "x", ")"}], ")"}]}], TraditionalForm]], "Input"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    SuperscriptBox["y", "\[Prime]",
     MultilineFunction->None], "(", "x", ")"}], " ", "=", 
   RowBox[{
    RowBox[{
     SuperscriptBox["f", "\[Prime]",
      MultilineFunction->None], "(", 
     RowBox[{"u", "(", "x", ")"}], ")"}], " ", 
    RowBox[{
     SuperscriptBox["u", "\[Prime]",
      MultilineFunction->None], "(", "x", ")"}]}]}], 
  TraditionalForm]], "Input"],

Cell["Ejemplo", "Text",
 FontSize->16],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"u", "(", "x_", ")"}], ":=", " ", 
   RowBox[{"1", "-", 
    SuperscriptBox["x", "3"], " "}]}], TraditionalForm]], "Input"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"y", "(", "u_", ")"}], ":=", 
   SuperscriptBox["u", "5"]}], TraditionalForm]], "Input"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    SuperscriptBox["y", "\[Prime]",
     MultilineFunction->None], "(", "u", ")"}], "=", " ", 
   RowBox[{"5", " ", 
    SuperscriptBox["u", "4"]}]}], TraditionalForm]], "Input"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    SuperscriptBox["u", "\[Prime]",
     MultilineFunction->None], "(", "x", ")"}], " ", "=", 
   RowBox[{
    RowBox[{"-", "3"}], " ", 
    SuperscriptBox["x", "2"]}]}], TraditionalForm]], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    SuperscriptBox["y", "\[Prime]",
     MultilineFunction->None], "(", 
    RowBox[{"u", "(", "x", ")"}], ")"}], " ", 
   RowBox[{
    SuperscriptBox["u", "\[Prime]",
     MultilineFunction->None], "(", "x", ")"}]}], TraditionalForm]], "Input"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"-", "15"}], " ", 
   SuperscriptBox["x", "2"], " ", 
   SuperscriptBox[
    RowBox[{"(", 
     RowBox[{"1", "-", 
      SuperscriptBox["x", "3"]}], ")"}], "4"]}], TraditionalForm]], "Output",
 FontSize->16]
}, Open  ]]
}, Closed]]
}, Closed]],

Cell[CellGroupData[{

Cell["Ejercicios propuestos", "Section",
 CellChangeTimes->{{3.5619012399001207`*^9, 3.561901256436344*^9}}],

Cell[CellGroupData[{

Cell[TextData[{
 "Calcula las derivada primera de las siguientes funciones:\na) f(x) = ",
 Cell[BoxData[
  FormBox[
   SuperscriptBox["x", "2"], TraditionalForm]]],
 " + sen 2x; b) f(x) = ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    SuperscriptBox["x", "3"], "-", 
    FractionBox["1", 
     SuperscriptBox["x", "2"]], "+", 
    RadicalBox[
     SuperscriptBox["x", "2"], "3"]}], TraditionalForm]]],
 "  ; c) f(x) = ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    SuperscriptBox["x", "3"], 
    SuperscriptBox["\[ExponentialE]", 
     RowBox[{"2", " ", "x"}]]}], TraditionalForm]]],
 "; d) f(x) = ",
 Cell[BoxData[
  FormBox[
   FractionBox[
    RowBox[{
     SuperscriptBox["x", "3"], "-", "x", "+", "1"}], 
    RowBox[{"2", "-", "x"}]], TraditionalForm]]],
 "; e) f(x) = ",
 Cell[BoxData[
  FormBox["ln", TraditionalForm]]],
 " ",
 Cell[BoxData[
  FormBox[
   FractionBox[
    RowBox[{"x", "+", "1"}], 
    RowBox[{"x", "-", "1"}]], TraditionalForm]]],
 "; f) ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    RowBox[{"f", "(", "x", ")"}], " ", "=", 
    SuperscriptBox["\[ExponentialE]", 
     RowBox[{"sen", " ", "3", "x"}]]}], TraditionalForm]]],
 "; g)",
 Cell[BoxData[
  FormBox[
   RowBox[{" ", 
    RowBox[{
     RowBox[{"f", "(", "x", ")"}], "=", 
     RowBox[{
      SqrtBox["x"], " ", 
      SuperscriptBox["\[ExponentialE]", 
       RowBox[{"sin", "(", 
        RowBox[{"3", " ", "x"}], ")"}]]}]}]}], TraditionalForm]],
  CellChangeTimes->{{3.5625868395813823`*^9, 3.562586855713023*^9}, {
    3.5625869556075068`*^9, 3.5625870463595257`*^9}, 3.5625888971717253`*^9, {
    3.562597642134124*^9, 3.5625976537718735`*^9}}]
}], "Subsection",
 CellChangeTimes->{{3.561902051947322*^9, 3.5619020864081583`*^9}, {
   3.561902219124187*^9, 3.561902447386024*^9}, 3.5625920939408417`*^9, {
   3.562597766701721*^9, 3.562597783456336*^9}}],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"f", "(", "x_", ")"}], ":=", 
   RowBox[{
    SuperscriptBox["x", "2"], "+", 
    RowBox[{"sin", "(", 
     RowBox[{"2", " ", "x"}], ")"}]}]}], TraditionalForm]], "Input",
 CellChangeTimes->{{3.562586579783228*^9, 3.562586619650426*^9}, 
   3.5625878648967776`*^9, {3.5625879439807816`*^9, 3.562587944464428*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"f", "'"}], "[", "x", "]"}]], "Input",
 CellChangeTimes->{{3.5625866268426733`*^9, 3.562586631757083*^9}}],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"2", " ", "x"}], "+", 
   RowBox[{"2", " ", 
    RowBox[{"cos", "(", 
     RowBox[{"2", " ", "x"}], ")"}]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{3.562586637420355*^9, 3.5625879157420664`*^9, 
  3.5625880559995513`*^9, 3.562592064891593*^9}]
}, Open  ]],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"f", "(", "x_", ")"}], ":=", 
   RowBox[{
    SuperscriptBox["x", "3"], "+", 
    RadicalBox[
     SuperscriptBox["x", "2"], "3"], "-", 
    FractionBox["1", 
     SuperscriptBox["x", "2"]]}]}], TraditionalForm]], "Input",
 CellChangeTimes->{{3.56258665584549*^9, 3.562586700574417*^9}, 
   3.562586730950148*^9, 3.5625880866553774`*^9}],

Cell[BoxData[
 FormBox[
  RowBox[{"que", " ", "tambi\[EAcute]n", " ", "podemos", " ", 
   RowBox[{"escribir", " ", ":"}]}], TraditionalForm]], "Text",
 CellChangeTimes->{{3.56258665584549*^9, 3.562586700574417*^9}, 
   3.562586730950148*^9, 3.5625880866553774`*^9, {3.5625881884336915`*^9, 
   3.5625882391044407`*^9}, {3.5625883635160275`*^9, 3.5625883778371744`*^9}}],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"f", "(", "x_", ")"}], ":=", 
   RowBox[{
    SuperscriptBox["x", "3"], "+", 
    SuperscriptBox["x", 
     RowBox[{"2", "/", "3"}]], "-", 
    SuperscriptBox["x", 
     RowBox[{"-", "2"}]]}]}], TraditionalForm]], "Input",
 CellChangeTimes->{{3.56258665584549*^9, 3.562586700574417*^9}, 
   3.562586730950148*^9, 3.5625880866553774`*^9, 3.5625883421900077`*^9}],

Cell[TextData[{
 "aplicar la derivada de ",
 Cell[BoxData[
  FormBox[
   SuperscriptBox["x", "a"], TraditionalForm]]],
 " que es: ",
 Cell[BoxData[
  FormBox["a", TraditionalForm]]],
 " ",
 Cell[BoxData[
  FormBox[
   SuperscriptBox["x", 
    RowBox[{"a", "-", "1"}]], TraditionalForm]]],
 ", recordar que ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    RadicalBox[
     SuperscriptBox["x", "b"], "a"], " ", "=", " ", 
    SuperscriptBox["x", 
     RowBox[{"b", "/", "a"}]]}], TraditionalForm]]]
}], "Text",
 CellChangeTimes->{{3.562596803420843*^9, 3.5625968650413613`*^9}, {
  3.562596964289834*^9, 3.5625969910909777`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"f", "'"}], "[", "x", "]"}]], "Input",
 CellChangeTimes->{{3.562586789719947*^9, 3.56258679184171*^9}, {
  3.562588319787546*^9, 3.562588349413085*^9}}],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox["2", 
    SuperscriptBox["x", "3"]], "+", 
   RowBox[{"3", " ", 
    SuperscriptBox["x", "2"]}], "+", 
   FractionBox["2", 
    RowBox[{"3", " ", 
     RadicalBox["x", "3"]}]]}], TraditionalForm]], "Output",
 CellChangeTimes->{3.5625883532196317`*^9, 3.5625922248467803`*^9}]
}, Open  ]],

Cell[BoxData[
 FormBox["", TraditionalForm]], "Text",
 CellChangeTimes->{{3.562596938877108*^9, 3.5625969623554087`*^9}}],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"f", "(", "x_", ")"}], ":=", 
   RowBox[{
    SuperscriptBox["x", "2"], " ", 
    SuperscriptBox["\[ExponentialE]", 
     RowBox[{"2", " ", "x"}]]}]}], TraditionalForm]], "Input",
 CellChangeTimes->{{3.5625868395813823`*^9, 3.562586855713023*^9}, 
   3.5625884206443977`*^9}],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"es", " ", "un", " ", "producto", " ", "por", " ", 
    RowBox[{"tanto", ":", " ", "\[IndentingNewLine]", 
     RowBox[{"f", "(", "x", ")"}]}]}], "=", 
   RowBox[{
    RowBox[{
     RowBox[{"g", "(", "x", ")"}], " ", 
     RowBox[{
      SuperscriptBox["h", "\[Prime]",
       MultilineFunction->None], "(", "x", ")"}]}], "+", 
    RowBox[{
     RowBox[{"h", "(", "x", ")"}], " ", 
     RowBox[{
      SuperscriptBox["g", "\[Prime]",
       MultilineFunction->None], "(", "x", ")"}]}]}]}], 
  TraditionalForm]], "Text",
 CellChangeTimes->{
  3.561989271220721*^9, {3.562588486446463*^9, 3.5625885019063606`*^9}, {
   3.5625885650875754`*^9, 3.562588593308518*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"f", "'"}], "[", "x", "]"}]], "Input",
 CellChangeTimes->{{3.562586789719947*^9, 3.56258679184171*^9}}],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"2", " ", 
    SuperscriptBox["\[ExponentialE]", 
     RowBox[{"2", " ", "x"}]], " ", 
    SuperscriptBox["x", "2"]}], "+", 
   RowBox[{"2", " ", 
    SuperscriptBox["\[ExponentialE]", 
     RowBox[{"2", " ", "x"}]], " ", "x"}]}], TraditionalForm]], "Output",
 CellChangeTimes->{3.5625868853241005`*^9, 3.5625885349321957`*^9}]
}, Open  ]],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"f", "(", "x_", ")"}], ":=", 
   FractionBox[
    RowBox[{
     SuperscriptBox["x", "3"], "-", "x", "+", "1"}], 
    RowBox[{"2", "-", "x"}]]}], TraditionalForm]], "Input",
 CellChangeTimes->{{3.5625868395813823`*^9, 3.562586855713023*^9}, {
  3.5625869556075068`*^9, 3.5625869774491863`*^9}, {3.5625886327460766`*^9, 
  3.562588638876994*^9}}],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    RowBox[{
     SuperscriptBox["f", "\[Prime]",
      MultilineFunction->None], "(", "x", ")"}], " ", "=", 
    FractionBox[
     RowBox[{
      RowBox[{
       RowBox[{
        SuperscriptBox["h", "\[Prime]",
         MultilineFunction->None], "(", "x", ")"}], 
       RowBox[{"g", "(", "x", ")"}]}], "-", 
      RowBox[{
       RowBox[{"h", "(", "x", ")"}], " ", 
       RowBox[{
        SuperscriptBox["g", "\[Prime]",
         MultilineFunction->None], "(", "x", ")"}]}]}], 
     SuperscriptBox[
      RowBox[{"g", "(", "x", ")"}], "2"]]}], ",", " ", 
   RowBox[{
    RowBox[{"con", " ", 
     RowBox[{"h", "(", "x", ")"}]}], " ", "=", " ", 
    RowBox[{
     RowBox[{
      SuperscriptBox["x", "3"], "-", "x", "+", 
      RowBox[{"1", " ", "y", " ", 
       RowBox[{"g", "(", "x", ")"}]}]}], " ", "=", 
     RowBox[{"2", "-", "x"}]}]}]}], TraditionalForm]], "Text",
 CellChangeTimes->{{3.5611225818015995`*^9, 3.561122652080221*^9}, {
  3.561989582851882*^9, 3.5619895839438963`*^9}, {3.5619896361577654`*^9, 
  3.5619896510559564`*^9}, {3.5625887542718554`*^9, 3.562588777079348*^9}, {
  3.562597126719116*^9, 3.562597158512324*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"f", "'"}], "[", "x", "]"}]], "Input",
 CellChangeTimes->{{3.5625887964860983`*^9, 3.5625888007294345`*^9}}],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{
     SuperscriptBox["x", "3"], "-", "x", "+", "1"}], 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{"2", "-", "x"}], ")"}], "2"]], "+", 
   FractionBox[
    RowBox[{
     RowBox[{"3", " ", 
      SuperscriptBox["x", "2"]}], "-", "1"}], 
    RowBox[{"2", "-", "x"}]]}], TraditionalForm]], "Output",
 CellChangeTimes->{3.5625888050507727`*^9}]
}, Open  ]],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"f", "(", "x_", ")"}], ":=", 
   RowBox[{"log", "(", 
    FractionBox[
     RowBox[{"x", "+", "1"}], 
     RowBox[{"x", "-", "1"}]], ")"}]}], TraditionalForm]], "Input",
 CellChangeTimes->{{3.5625868395813823`*^9, 3.562586855713023*^9}, {
   3.5625869556075068`*^9, 3.562587016514591*^9}, 3.5625886747888365`*^9}],

Cell[BoxData[{
 FormBox[
  RowBox[{
   RowBox[{
    FractionBox["1", 
     RowBox[{"g", "(", "x", ")"}]], 
    RowBox[{"g", "'"}], 
    RowBox[{"(", "x", ")"}]}], " "}], TraditionalForm], "\[IndentingNewLine]", 
 FormBox[
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"con", " ", 
      RowBox[{"g", "(", "x", ")"}]}], "=", 
     FractionBox[
      RowBox[{"x", "+", "1"}], 
      RowBox[{"x", "-", "1"}]]}], ",", "y"}], " "}], 
  TraditionalForm], "\[IndentingNewLine]", 
 FormBox[
  RowBox[{
   RowBox[{
    RowBox[{"g", "'"}], 
    RowBox[{"(", "x", ")"}]}], "=", 
   RowBox[{
    FractionBox[
     RowBox[{"x", "-", "1"}], 
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{"x", "-", "1"}], ")"}], "2"]], "-", 
    FractionBox[
     RowBox[{"x", "+", "1"}], 
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{"x", "-", "1"}], ")"}], "2"]]}]}], TraditionalForm]}], "Text",
 CellChangeTimes->{{3.5625890558288107`*^9, 3.5625891217717323`*^9}, {
  3.562593012898817*^9, 3.5625930693095016`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"f", "'"}], "[", "x", "]"}], "//", "Simplify"}]], "Input",
 CellChangeTimes->{{3.562589164367353*^9, 3.5625891942887287`*^9}}],

Cell[BoxData[
 FormBox[
  RowBox[{"-", 
   FractionBox["2", 
    RowBox[{
     SuperscriptBox["x", "2"], "-", "1"}]]}], TraditionalForm]], "Output",
 CellChangeTimes->{{3.5625891691878457`*^9, 3.56258919489714*^9}}]
}, Open  ]],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"f", "(", "x_", ")"}], ":=", 
   SuperscriptBox["\[ExponentialE]", 
    RowBox[{"sin", "(", 
     RowBox[{"3", " ", "x"}], ")"}]]}], TraditionalForm]], "Input",
 CellChangeTimes->{{3.5625868395813823`*^9, 3.562586855713023*^9}, {
   3.5625869556075068`*^9, 3.5625870463595257`*^9}, 3.5625888971717253`*^9}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"f", "'"}], "[", "x", "]"}]], "Input",
 CellChangeTimes->{{3.562589164367353*^9, 3.5625891942887287`*^9}, 
   3.562589234771507*^9}],

Cell[BoxData[
 FormBox[
  RowBox[{"3", " ", 
   SuperscriptBox["\[ExponentialE]", 
    RowBox[{"sin", "(", 
     RowBox[{"3", " ", "x"}], ")"}]], " ", 
   RowBox[{"cos", "(", 
    RowBox[{"3", " ", "x"}], ")"}]}], TraditionalForm]], "Output",
 CellChangeTimes->{3.5625892383127747`*^9}]
}, Open  ]],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"f", "(", "x_", ")"}], ":=", 
   RowBox[{
    SqrtBox["x"], " ", 
    SuperscriptBox["\[ExponentialE]", 
     RowBox[{"sin", "(", 
      RowBox[{"3", " ", "x"}], ")"}]]}]}], TraditionalForm]], "Input",
 CellChangeTimes->{{3.5625868395813823`*^9, 3.562586855713023*^9}, {
   3.5625869556075068`*^9, 3.5625870463595257`*^9}, 3.5625888971717253`*^9, {
   3.562597642134124*^9, 3.5625976537718735`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"f", "'"}], "[", "x", "]"}]], "Input",
 CellChangeTimes->{{3.562589164367353*^9, 3.5625891942887287`*^9}, 
   3.562589234771507*^9}],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    SuperscriptBox["\[ExponentialE]", 
     RowBox[{"sin", "(", 
      RowBox[{"3", " ", "x"}], ")"}]], 
    RowBox[{"2", " ", 
     SqrtBox["x"]}]], "+", 
   RowBox[{"3", " ", 
    SqrtBox["x"], " ", 
    SuperscriptBox["\[ExponentialE]", 
     RowBox[{"sin", "(", 
      RowBox[{"3", " ", "x"}], ")"}]], " ", 
    RowBox[{"cos", "(", 
     RowBox[{"3", " ", "x"}], ")"}]}]}], TraditionalForm]], "Output",
 CellChangeTimes->{3.5625977453762474`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell["Paso a paso", "Subsubsection",
 CellChangeTimes->{{3.5625870705713463`*^9, 3.5625870768895082`*^9}, {
  3.5628234302069645`*^9, 3.5628234356466713`*^9}}],

Cell[BoxData[
 GraphicsBox[
  TagBox[RasterBox[CompressedData["
1:eJzs3XdcU/f+P/DDiCLLAAoylCEguCGKo+BobRXFPaq22lpse9va1lHvt7WV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    "], {{0, 368}, {656, 0}}, {0, 255},
    ColorFunction->RGBColor],
   BoxForm`ImageTag["Byte", ColorSpace -> "RGB", Interleaving -> True],
   Selectable->False],
  BaseStyle->"ImageGraphics",
  ImageSize->Automatic,
  ImageSizeRaw->{656, 368},
  PlotRange->{{0, 656}, {0, 368}}]], "Text",
 CellChangeTimes->{3.561901268370524*^9}],

Cell["Reproduzca los mismos ejemplos con Mathematica", "Text",
 CellChangeTimes->{{3.562044491005808*^9, 3.562044514952834*^9}, 
   3.5620445495853353`*^9}]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell[TextData[{
 "Halla la funci\[OAcute]n derivada de ",
 Cell[BoxData[
  FormBox[
   TagBox[GridBox[{
      {"\[Piecewise]", GridBox[{
         {
          FractionBox["1", 
           RowBox[{"x", "-", "2"}]], 
          RowBox[{
           RowBox[{"para", " ", "x"}], "<", "2"}]},
         {
          RowBox[{
           SuperscriptBox["x", "2"], "-", "4"}], 
          RowBox[{
           RowBox[{"para", " ", "x"}], "\[GreaterEqual]", "2"}]}
        },
        AllowedDimensions->{2, Automatic},
        Editable->True,
        GridBoxAlignment->{
         "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
        GridBoxItemSize->{
         "Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}},
           "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.84]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}},
        Selectable->True]}
     },
     GridBoxAlignment->{
      "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
       "RowsIndexed" -> {}},
     GridBoxItemSize->{
      "Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, 
       "RowsIndexed" -> {}},
     GridBoxSpacings->{"Columns" -> {
         Offset[0.27999999999999997`], {
          Offset[0.35]}, 
         Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
         Offset[0.2], {
          Offset[0.4]}, 
         Offset[0.2]}, "RowsIndexed" -> {}}],
    "Piecewise",
    DeleteWithContents->True,
    Editable->False,
    SelectWithContents->True,
    Selectable->False], TraditionalForm]]]
}], "Subsection",
 CellChangeTimes->{{3.5619024819281907`*^9, 3.561902592615509*^9}, {
  3.5619026277783527`*^9, 3.5619026427544775`*^9}, {3.562589523110161*^9, 
  3.5625895657296343`*^9}}],

Cell[BoxData[
 GraphicsBox[
  TagBox[RasterBox[CompressedData["
1:eJztvQlUU0cb/38VUASUsAhC2DdFRYVQFeoCLq+iuOBe7SrVtlbtq1a7U6t2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    "], {{0, 187}, {637, 0}}, {0, 255},
    ColorFunction->RGBColor],
   BoxForm`ImageTag["Byte", ColorSpace -> "RGB", Interleaving -> True],
   Selectable->False],
  BaseStyle->"ImageGraphics",
  ImageSize->Automatic,
  ImageSizeRaw->{637, 187},
  PlotRange->{{0, 637}, {0, 187}}]], "Text",
 CellChangeTimes->{3.5619013543550043`*^9}],

Cell["Reproducimos el mismo ejemplo con Mathematica", "Text",
 CellChangeTimes->{{3.562044491005808*^9, 3.5620445407291317`*^9}, {
  3.562823685594366*^9, 3.562823745171339*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"f", "[", "x_", "]"}], ":=", 
  TagBox[GridBox[{
     {"\[Piecewise]", GridBox[{
        {
         FractionBox["1", 
          RowBox[{"x", "-", "2"}]], 
         RowBox[{"x", "<", "2"}]},
        {
         RowBox[{
          SuperscriptBox["x", "2"], "-", "2"}], 
         RowBox[{"x", "\[GreaterEqual]", "2"}]}
       },
       AllowedDimensions->{2, Automatic},
       Editable->True,
       GridBoxAlignment->{
        "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
          "RowsIndexed" -> {}},
       GridBoxItemSize->{
        "Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, 
         "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.84]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}},
       Selectable->True]}
    },
    GridBoxAlignment->{
     "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
      "RowsIndexed" -> {}},
    GridBoxItemSize->{
     "Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, 
      "RowsIndexed" -> {}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.35]}, 
        Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}, "RowsIndexed" -> {}}],
   "Piecewise",
   DeleteWithContents->True,
   Editable->False,
   SelectWithContents->True,
   Selectable->False]}]], "Input",
 CellChangeTimes->{{3.562823479044197*^9, 3.562823489818542*^9}, {
  3.5628235269773216`*^9, 3.5628235887881007`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"f", "'"}], "[", "x", "]"}]], "Input",
 CellChangeTimes->{{3.562823642631521*^9, 3.5628236448779078`*^9}}],

Cell[BoxData[
 FormBox[
  TagBox[GridBox[{
     {"\[Piecewise]", GridBox[{
        {
         RowBox[{"-", 
          FractionBox["1", 
           SuperscriptBox[
            RowBox[{"(", 
             RowBox[{"x", "-", "2"}], ")"}], "2"]]}], 
         RowBox[{"x", "<", "2"}]},
        {
         RowBox[{"2", " ", "x"}], 
         RowBox[{"x", ">", "2"}]},
        {"Indeterminate", 
         TagBox["True",
          "PiecewiseDefault",
          AutoDelete->True]}
       },
       AllowedDimensions->{2, Automatic},
       Editable->True,
       GridBoxAlignment->{
        "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
          "RowsIndexed" -> {}},
       GridBoxItemSize->{
        "Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, 
         "RowsIndexed" -> {}},
       GridBoxSpacings->{"Columns" -> {
           Offset[0.27999999999999997`], {
            Offset[0.84]}, 
           Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
           Offset[0.2], {
            Offset[0.4]}, 
           Offset[0.2]}, "RowsIndexed" -> {}},
       Selectable->True]}
    },
    GridBoxAlignment->{
     "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
      "RowsIndexed" -> {}},
    GridBoxItemSize->{
     "Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, 
      "RowsIndexed" -> {}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.35]}, 
        Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}, "RowsIndexed" -> {}}],
   "Piecewise",
   DeleteWithContents->True,
   Editable->False,
   SelectWithContents->True,
   Selectable->False], TraditionalForm]], "Output",
 CellChangeTimes->{3.562823653239592*^9}]
}, Open  ]]
}, Closed]]
}, Closed]],

Cell[CellGroupData[{

Cell["Concepto de diferencial", "Section",
 CellChangeTimes->{{3.5628238916880546`*^9, 3.5628239107982492`*^9}, {
  3.562824334951026*^9, 3.5628243424703355`*^9}}],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"Diferencial", ".", 
      RowBox[{"-", " ", "En"}]}], " ", "la", " ", "definicion", " ", "de", 
     " ", "derivada", " ", 
     RowBox[{"f", " ", "'"}], 
     RowBox[{"(", "x", ")"}]}], "=", 
    RowBox[{
     FractionBox["dy", "dx"], "=", 
     RowBox[{
      RowBox[{
       UnderscriptBox["lim", 
        RowBox[{"x", "\[Rule]", "a"}]], "\[ThinSpace]", 
       FractionBox[
        RowBox[{
         RowBox[{"f", "(", "x", ")"}], "-", 
         RowBox[{"f", "(", "a", ")"}]}], 
        RowBox[{"x", "-", "a"}]]}], "=", 
      RowBox[{
       UnderscriptBox["lim", 
        RowBox[{"\[CapitalDelta]x", "\[Rule]", "0"}]], "\[ThinSpace]", 
       RowBox[{
        FractionBox[
         RowBox[{
          RowBox[{"f", "(", 
           RowBox[{"x", "+", "\[CapitalDelta]x"}], ")"}], "-", 
          RowBox[{"f", "(", "x", ")"}]}], "\[CapitalDelta]x"], " ", 
        "despejamos", " ", "dy"}]}]}]}]}], " ", ",", " ", 
   RowBox[{
   "que", " ", "denominamos", " ", "diferencial", " ", "de", " ", "y"}], ",", 
   " ", 
   RowBox[{"nos", " ", "queda"}]}], TraditionalForm]], "Text",
 CellChangeTimes->{{3.5612107823038387`*^9, 3.561210782952946*^9}, {
   3.5612108180094957`*^9, 3.561210939461776*^9}, 3.5612109956786475`*^9, {
   3.5612112507199926`*^9, 3.5612113270000715`*^9}, {3.5612117305399036`*^9, 
   3.561211818867133*^9}, {3.562045259859214*^9, 3.562045273878961*^9}, {
   3.562824119575199*^9, 3.562824168809328*^9}, {3.5628242027240644`*^9, 
   3.5628242167018013`*^9}, {3.5628242481517296`*^9, 
   3.5628242492437415`*^9}, {3.5628242935950365`*^9, 3.562824326121334*^9}},
 FontSize->16],

Cell[BoxData[{
 FormBox[
  RowBox[{"dy", " ", "=", 
   RowBox[{
    RowBox[{
     RowBox[{
      RowBox[{
       UnderscriptBox[
        RowBox[{" ", "lim"}], 
        RowBox[{"\[CapitalDelta]x", "\[Rule]", "0"}]], " ", 
       RowBox[{"f", "(", 
        RowBox[{
         SubscriptBox["x", "0"], "+", "\[CapitalDelta]x"}], ")"}]}], " ", "-", 
      RowBox[{"f", "(", 
       SubscriptBox["x", "0"], ")"}]}], " ", "\[Rule]", "dy"}], " ", "=", " ", 
    RowBox[{
     RowBox[{"f", "'"}], 
     RowBox[{"(", 
      SubscriptBox["x", "0"], ")"}], " ", "dx", Cell[""]}]}]}], 
  TraditionalForm], "\[IndentingNewLine]", 
 FormBox[
  RowBox[{"Aproximaci\[OAcute]n", " "}], 
  TraditionalForm], "\[IndentingNewLine]", 
 FormBox[
  RowBox[{"\[CapitalDelta]y", " ", "\[TildeEqual]", " ", 
   RowBox[{
    RowBox[{"f", "'"}], 
    RowBox[{"(", 
     SubscriptBox["x", "0"], ")"}], " ", "\[CapitalDelta]x", Cell[""]}]}], 
  TraditionalForm]}], "Text",
 CellChangeTimes->{{3.562824183067872*^9, 3.562824191398344*^9}, {
  3.562824241724533*^9, 3.562824243440528*^9}},
 FontSize->16],

Cell[CellGroupData[{

Cell[TextData[{
 "Ejemplo: Dado un cuadrado de lado ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "0"], TraditionalForm]]],
 "= 1 m. \[DownQuestion]Cuanto se increntar\[AAcute] el area si el aumentamos \
la longitud de lado 0.1 m?, \[DownQuestion]y si lo aumentamos 0.01 m?."
}], "Subsubsection",
 FontSize->16],

Cell["M\[EAcute]todo exacto", "Text",
 FontSize->16],

Cell[BoxData[{
 FormBox[
  RowBox[{
   RowBox[{
    RowBox[{"S", " ", "=", " ", 
     RowBox[{
      RowBox[{
       SuperscriptBox["x", "2"], "\[Rule]", "\[CapitalDelta]S"}], " ", "=", 
      RowBox[{
       SuperscriptBox[
        RowBox[{"(", 
         RowBox[{
          SubscriptBox["x", "0"], "+", 
          RowBox[{"\[CapitalDelta]", " ", 
           SubscriptBox["x", "0"]}]}], ")"}], "2"], "-", 
       SuperscriptBox[
        SubscriptBox["x", "0"], "2"]}]}]}], " ", ";"}], " "}], 
  TraditionalForm], "\[IndentingNewLine]", 
 FormBox[
  RowBox[{
   RowBox[{
    RowBox[{"para", " ", "\[CapitalDelta]", " ", 
     SubscriptBox["x", "0"]}], "=", " ", 
    RowBox[{
     RowBox[{"0.1", " ", "\[Rule]", "   ", 
      RowBox[{
       SuperscriptBox["1.1", "2"], "-", "1"}]}], " ", "=", " ", "0.21"}]}], 
   ";"}], TraditionalForm], "\[IndentingNewLine]", 
 FormBox[
  RowBox[{
   RowBox[{"para", " ", "\[CapitalDelta]", " ", 
    SubscriptBox["x", "0"]}], "=", " ", 
   RowBox[{
    RowBox[{"0.01", "\[Rule]", 
     RowBox[{
      SuperscriptBox["1.01", "2"], "-", "1"}]}], " ", "=", " ", 
    "0.020100000000000007`"}]}], TraditionalForm]}], "Text",
 FontSize->16],

Cell["M\[EAcute]todo aproximado ", "Text",
 FontSize->16],

Cell[BoxData[{
 FormBox[
  RowBox[{
   RowBox[{
    RowBox[{"S", " ", "=", " ", 
     SuperscriptBox["x", "2"]}], ",", " ", 
    RowBox[{
     RowBox[{
      RowBox[{
       RowBox[{
        RowBox[{"usamos", " ", "\[CapitalDelta]y"}], " ", "\[TildeEqual]", 
        " ", 
        RowBox[{
         RowBox[{"f", "'"}], 
         RowBox[{"(", 
          SubscriptBox["x", "0"], ")"}], " ", "\[CapitalDelta]x", Cell[
         ""]}]}], "\[Rule]", "\[CapitalDelta]S"}], " ", "=", 
      RowBox[{"2", " ", 
       SubscriptBox["x", "0"], " ", "\[CapitalDelta]x", Cell[""]}]}], " ", 
     ";"}]}], " "}], TraditionalForm], "\[IndentingNewLine]", 
 FormBox[
  RowBox[{
   RowBox[{
    RowBox[{"para", " ", "\[CapitalDelta]", " ", 
     SubscriptBox["x", "0"]}], "=", " ", 
    RowBox[{
     RowBox[{"0.1", " ", "\[Rule]", "   ", 
      RowBox[{"2", "\[Times]", "1", "\[Times]", "0.1"}]}], " ", "=", " ", 
     "0.2"}]}], ";"}], TraditionalForm], "\[IndentingNewLine]", 
 FormBox[
  RowBox[{
   RowBox[{"para", " ", "\[CapitalDelta]", " ", 
    SubscriptBox["x", "0"]}], "=", " ", 
   RowBox[{
    RowBox[{"0.01", "\[Rule]", 
     RowBox[{"2", "\[Times]", "1", "\[Times]", "0.01"}]}], " ", "=", " ", 
    "0.02"}]}], TraditionalForm]}], "Text",
 FontSize->16],

Cell["\<\
Comparaci\[OAcute]n m\[EAcute]todo exacto con m\[EAcute]todo aproximado. \
Observese que el error relativo disminuye cuando el incremento se va haciendo \
mas peque\[NTilde]o\
\>", "Text",
 FontSize->16],

Cell["(0.21-0.20)/0.21\[TildeEqual]5.0%", "Text",
 FontSize->16],

Cell["(0.0201-0.02)/0.0201\[TildeEqual] 0.5%", "Text",
 FontSize->16]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell["\<\
EJEMPLOS PARA ILUSTRAR LA APLICACI\[CapitalOAcute]N DE DERIVADAS EN EC\
\[CapitalOAcute]NOMIA\
\>", "Section",
 CellChangeTimes->{{3.5610179919424405`*^9, 3.561017997405125*^9}, {
  3.561210306893659*^9, 3.561210313416066*^9}, {3.5612135319765577`*^9, 
  3.561213541447305*^9}, {3.5612136398880806`*^9, 3.561213657800419*^9}}],

Cell[CellGroupData[{

Cell["\<\
Ejemplo 1.- Explotaci\[OAcute]n de un pozo de petroleo\
\>", "Subsection",
 CellChangeTimes->{{3.562044626698181*^9, 3.562044639744818*^9}}],

Cell[TextData[{
 "De un pozo de petroleo el coste ",
 Cell[BoxData[
  FormBox[
   RowBox[{"c", "(", "t", ")"}], TraditionalForm]]],
 " de extracci\[OAcute]n unitario (en $/barril) aumenta \
(inflaci\[OAcute]n,..)  con el tiempo ",
 Cell[BoxData[
  FormBox["t", TraditionalForm]]],
 " (en a\[NTilde]os) de acuerdo a"
}], "Text"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"c", "(", "t_", ")"}], ":=", 
   RowBox[{
    RowBox[{"0.1", " ", 
     SuperscriptBox["t", "1.5"]}], "+", "10"}]}], TraditionalForm]], "Input"],

Cell[TextData[{
 "El  volumen diario, ",
 Cell[BoxData[
  FormBox[
   RowBox[{"q", "(", "t", ")"}], TraditionalForm]]],
 ",   (en barriles) extraido  disminuye de acuerdo a "
}], "Text"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"q", "(", "t_", ")"}], ":=", 
   RowBox[{
    SuperscriptBox["10", "5"], " ", 
    SuperscriptBox["\[ExponentialE]", 
     RowBox[{
      RowBox[{"-", " ", "0.05"}], " ", "t"}]]}]}], TraditionalForm]], "Input"],

Cell["\<\
Obs\[EAcute]rvese la variaci\[OAcute]n del coste unitario y de los gastos \
totales anuales con el tiempo: {a\[NTilde]o, $/barril}\
\>", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
 FormBox[
  RowBox[{"TableForm", "[", 
   RowBox[{"Table", "[", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"t", ",", 
       RowBox[{"c", "(", "t", ")"}], ",", 
       RowBox[{"q", "(", "t", ")"}]}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"t", ",", "0", ",", "10"}], "}"}]}], "]"}], "]"}], 
  TraditionalForm]], "Input"],

Cell[BoxData[
 FormBox[
  TagBox[GridBox[{
     {"0", "10.`", "100000.`"},
     {"1", "10.1`", "95122.94245007141`"},
     {"2", "10.282842712474618`", "90483.74180359596`"},
     {"3", "10.519615242270664`", "86070.79764250579`"},
     {"4", "10.8`", "81873.07530779818`"},
     {"5", "11.118033988749895`", "77880.07830714049`"},
     {"6", "11.469693845669907`", "74081.8220681718`"},
     {"7", "11.852025917745213`", "70468.80897187135`"},
     {"8", "12.262741699796953`", "67032.00460356394`"},
     {"9", "12.7`", "63762.815162177336`"},
     {"10", "13.16227766016838`", "60653.06597126334`"}
    },
    GridBoxAlignment->{
     "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
      "RowsIndexed" -> {}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[2.0999999999999996`]}, 
        Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}, "RowsIndexed" -> {}}],
   Function[BoxForm`e$, 
    TableForm[BoxForm`e$]]], TraditionalForm]], "Output",
 CellChangeTimes->{{3.561210253896897*^9, 3.5612102781228523`*^9}}]
}, Open  ]],

Cell["\<\
El coste de producci\[OAcute]n , en $/a\[NTilde]o, con el tiempo (en a\
\[NTilde]os) ser\[AAcute]:  \
\>", "Text"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"G", "(", "t_", ")"}], ":=", 
   RowBox[{
    RowBox[{"c", "(", "t", ")"}], " ", 
    RowBox[{"q", "(", "t", ")"}]}]}], TraditionalForm]], "Input"],

Cell[TextData[{
 "El coste de producci\[OAcute]n marginal (tasa de variaci\[OAcute]n) ser\
\[AAcute]:\n",
 Cell[BoxData[
  FormBox[
   RowBox[{
    SuperscriptBox["G", "\[Prime]",
     MultilineFunction->None], "(", "t", ")"}], TraditionalForm]]],
 " = ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    RowBox[{
     RowBox[{"q", "(", "t", ")"}], " ", 
     RowBox[{
      SuperscriptBox["c", "\[Prime]",
       MultilineFunction->None], "(", "t", ")"}]}], "+", 
    RowBox[{
     RowBox[{"c", "(", "t", ")"}], " ", 
     RowBox[{
      SuperscriptBox["q", "\[Prime]",
       MultilineFunction->None], "(", "t", ")"}]}]}], TraditionalForm]]],
 ", substituyendo se obtiene"
}], "Text"],

Cell[CellGroupData[{

Cell[BoxData[
 FormBox[
  RowBox[{
   SuperscriptBox["G", "\[Prime]",
    MultilineFunction->None], "(", "t", ")"}], TraditionalForm]], "Input"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"15000.000000000002`", " ", 
    SuperscriptBox["\[ExponentialE]", 
     RowBox[{
      RowBox[{"-", "0.05`"}], " ", "t"}]], " ", 
    SuperscriptBox["t", "0.5`"]}], "-", 
   RowBox[{"5000.`", " ", 
    SuperscriptBox["\[ExponentialE]", 
     RowBox[{
      RowBox[{"-", "0.05`"}], " ", "t"}]], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"0.1`", " ", 
       SuperscriptBox["t", "1.5`"]}], "+", "10"}], ")"}]}]}], 
  TraditionalForm]], "Output",
 CellChangeTimes->{{3.561210253959258*^9, 3.561210278185253*^9}}]
}, Open  ]],

Cell["\<\
La tasa proporcional de variaci\[OAcute]n ser\[AAcute]\
\>", "Text"],

Cell[TextData[{
 Cell[BoxData[
  FormBox[
   FractionBox[
    FormBox[
     RowBox[{
      SuperscriptBox["G", "\[Prime]",
       MultilineFunction->None], "(", "t", ")"}],
     TraditionalForm], 
    RowBox[{"G", "(", "t", ")"}]], TraditionalForm]]],
 " = ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    FractionBox[
     RowBox[{
      RowBox[{
       RowBox[{"q", "(", "t", ")"}], " ", 
       RowBox[{
        SuperscriptBox["c", "\[Prime]",
         MultilineFunction->None], "(", "t", ")"}]}], "+", 
      RowBox[{
       RowBox[{"c", "(", "t", ")"}], " ", 
       RowBox[{
        SuperscriptBox["q", "\[Prime]",
         MultilineFunction->None], "(", "t", ")"}]}]}], 
     RowBox[{
      RowBox[{"q", "(", "t", ")"}], " ", 
      RowBox[{"c", "(", "t", ")"}]}]], "=", 
    RowBox[{
     FractionBox[
      RowBox[{" ", 
       RowBox[{
        SuperscriptBox["c", "\[Prime]",
         MultilineFunction->None], "(", "t", ")"}]}], 
      RowBox[{"c", "(", "t", ")"}]], " ", "+", 
     FractionBox[
      RowBox[{" ", 
       RowBox[{
        SuperscriptBox["q", "\[Prime]",
         MultilineFunction->None], "(", "t", ")"}]}], 
      RowBox[{"q", "(", "t", ")"}]]}]}], TraditionalForm]]]
}], "Text"],

Cell[CellGroupData[{

Cell[BoxData[
 FormBox[
  FractionBox[
   RowBox[{
    SuperscriptBox["G", "\[Prime]",
     MultilineFunction->None], "(", "t", ")"}], 
   RowBox[{"G", "(", "t", ")"}]], TraditionalForm]], "Input"],

Cell[BoxData[
 FormBox[
  FractionBox[
   RowBox[{
    SuperscriptBox["\[ExponentialE]", 
     RowBox[{"0.05`", " ", "t"}]], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"15000.000000000002`", " ", 
       SuperscriptBox["\[ExponentialE]", 
        RowBox[{
         RowBox[{"-", "0.05`"}], " ", "t"}]], " ", 
       SuperscriptBox["t", "0.5`"]}], "-", 
      RowBox[{"5000.`", " ", 
       SuperscriptBox["\[ExponentialE]", 
        RowBox[{
         RowBox[{"-", "0.05`"}], " ", "t"}]], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"0.1`", " ", 
          SuperscriptBox["t", "1.5`"]}], "+", "10"}], ")"}]}]}], ")"}]}], 
   RowBox[{"100000", " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"0.1`", " ", 
       SuperscriptBox["t", "1.5`"]}], "+", "10"}], ")"}]}]], 
  TraditionalForm]], "Output",
 CellChangeTimes->{{3.561210254021659*^9, 3.561210278247658*^9}}]
}, Open  ]],

Cell["\<\
Supongamos que se espera que el precio unitario de venta ($/barril) varie de \
acuerdo a\
\>", "Text"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"r", "(", "t_", ")"}], ":=", 
   RowBox[{
    RowBox[{"0.05", " ", "t"}], "+", "18"}]}], TraditionalForm]], "Input"],

Cell[TextData[{
 "Por tanto, los ingresos totales anuales ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    RowBox[{"R", "(", "t", ")"}], " "}], TraditionalForm]]],
 "variar\[AAcute]n de acuerdo a"
}], "Text"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"R", "(", "t_", ")"}], ":=", 
   RowBox[{
    RowBox[{"r", "(", "t", ")"}], " ", 
    RowBox[{"q", "(", "t", ")"}]}]}], TraditionalForm]], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
 FormBox[
  RowBox[{"R", "(", "t", ")"}], TraditionalForm]], "Input"],

Cell[BoxData[
 FormBox[
  RowBox[{"100000", " ", 
   SuperscriptBox["\[ExponentialE]", 
    RowBox[{
     RowBox[{"-", "0.05`"}], " ", "t"}]], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{"0.05`", " ", "t"}], "+", "18"}], ")"}]}], 
  TraditionalForm]], "Output",
 CellChangeTimes->{{3.5612102540997133`*^9, 3.5612102783256545`*^9}}]
}, Open  ]],

Cell["El ingreso marginal sera", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
 FormBox[
  RowBox[{
   SuperscriptBox["R", "\[Prime]",
    MultilineFunction->None], "(", "t", ")"}], TraditionalForm]], "Input"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"5000.`", " ", 
    SuperscriptBox["\[ExponentialE]", 
     RowBox[{
      RowBox[{"-", "0.05`"}], " ", "t"}]]}], "-", 
   RowBox[{"5000.`", " ", 
    SuperscriptBox["\[ExponentialE]", 
     RowBox[{
      RowBox[{"-", "0.05`"}], " ", "t"}]], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"0.05`", " ", "t"}], "+", "18"}], ")"}]}]}], 
  TraditionalForm]], "Output",
 CellChangeTimes->{{3.561210254166065*^9, 3.5612102783724546`*^9}}]
}, Open  ]],

Cell[TextData[{
 "Nos planteamos: \[DownQuestion]Cual ser\[AAcute] el beneficio anual ",
 Cell[BoxData[
  FormBox[
   RowBox[{"B", "(", "t", ")"}], TraditionalForm]]],
 "  esperado?"
}], "Text"],

Cell["Vendra dado por la diferencia entre ingresos y gastos", "Text"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"B", "(", "t_", ")"}], ":=", 
   RowBox[{
    RowBox[{"R", "(", "t", ")"}], "-", 
    RowBox[{"G", "(", "t", ")"}]}]}], TraditionalForm]], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
 FormBox[
  RowBox[{"B", "(", "t", ")"}], TraditionalForm]], "Input"],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"100000", " ", 
    SuperscriptBox["\[ExponentialE]", 
     RowBox[{
      RowBox[{"-", "0.05`"}], " ", "t"}]], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"0.05`", " ", "t"}], "+", "18"}], ")"}]}], "-", 
   RowBox[{"100000", " ", 
    SuperscriptBox["\[ExponentialE]", 
     RowBox[{
      RowBox[{"-", "0.05`"}], " ", "t"}]], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"0.1`", " ", 
       SuperscriptBox["t", "1.5`"]}], "+", "10"}], ")"}]}]}], 
  TraditionalForm]], "Output",
 CellChangeTimes->{{3.561210254223064*^9, 3.561210278450468*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 FormBox[
  RowBox[{"Simplify", "[", 
   RowBox[{"B", "(", "t", ")"}], "]"}], TraditionalForm]], "Input"],

Cell[BoxData[
 FormBox[
  RowBox[{
   SuperscriptBox["\[ExponentialE]", 
    RowBox[{
     RowBox[{"-", "0.05`"}], " ", "t"}]], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{"-", 
      RowBox[{"10000.`", " ", 
       SuperscriptBox["t", "1.5`"]}]}], "+", 
     RowBox[{"5000.`", " ", "t"}], "+", "800000.`"}], ")"}]}], 
  TraditionalForm]], "Output",
 CellChangeTimes->{{3.561210254332299*^9, 3.56121027849726*^9}}]
}, Open  ]],

Cell["\<\
Podemos observar que el beneficio anual va disminuyendo con el tiempo.\
\>", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{"B", "[", "t", "]"}], ",", " ", 
   RowBox[{"{", 
    RowBox[{"t", ",", " ", "0", ",", " ", "10"}], "}"}], ",", " ", 
   RowBox[{"PlotRange", "\[Rule]", " ", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"3", " ", 
       RowBox[{"10", "^", "5"}]}], ",", " ", 
      RowBox[{"9", " ", 
       RowBox[{"10", "^", "5"}]}]}], "}"}]}]}], "]"}]], "Input"],

Cell[BoxData[
 FormBox[
  GraphicsBox[{{}, {}, 
    {Hue[0.67, 0.6, 0.6], LineBox[CompressedData["
1:eJwVjG00VAkYgFmFGEr3+hxm7szFTBOlTad0Vvd9s1v5ahViabcMoXwUy26i
drdSbIempUQNkThpKVJnRaMmJV+jELW0K2MSKZWmjNRs++M5z3n+PDzxzo3b
vtDR0fH9zP+W7hPrL4k4siq7LGhGu12ITd2UTxC1nbE3dB5z+NzaO7IDFJXC
NJgHz/WMFqL0RhZ3NpXJ5PSF+/weKcRY9+S499x8Rs1mTn8SC7H7Q3TuK+55
JiVutLYxVIgG/UOCF9w65qioNaXHR4jFrUUJz7ktzIq9k17dzkKsupjZH7vo
b6bFit1gMSLAKOZ+/niiknlSODKPVSLAeNUCZW3VKGMmcZP7bRagEe+g4N8V
r5gY34+dSlMBZs9rExVvnWR+vmwZ4XnbEcX9AY167e8YqbZzX2CSIybcPije
KZhm8Pia4kHaEat3sfytPD8ylcdivrF76IDFqTFjLkE6cHTKXScg3QH3F81s
eDuuCzYGrtclyx1Qp3sQGvbowei7Kw3TY/bomBS5O0A0GxIqlOW5efY4rM7b
ZHxdHzr7H6/J9rRHL9WOvX8kGMK7uYXPet7SuH5YspDDMYK9kdMDOcU0jt0S
/3q30hjGHVhHnvvTuMis185jiwm09WVW1Wv5aMSowwYmTeHAzqVZ7tV8XPsi
5D0/cB5Ubr7mF7CZjw/lEbohTmagmeP60XEOH69kNP1Aqc1A4GrbLK/nYeTs
5EGFYj6wlx24ZxvNw/DE1CusAgJuLux76WnDw8VRCxU+YSQkPrkRvlZBYed8
J+NkN3NQNCpbRWkU1lftP+WkZwHlzuXew4spTNUV+bU/toDTlZwgj3ouGg3s
WRdfawmHSl2KC224qCrj5RalWUHTo9hjBekczBVaz6oLtAbZpY6XE8N2KCmI
bA6jbCC6QPTdP9/aYUju9wrWiA2w5vrmFMpscerrc5oiGRvmT8c0GvBtUala
vVt+2BbOSKtXjUnYWOK+hN0RZgcudIlL7VsbrExPNoty5sCgeWiFKtwGDweG
e+upOfBlTUXQ615rXDZQfP5wBxdkwRF1row1nlxwqrLDm4J9j/J2VddY4S83
sk5611Gg/1fIpXNsK/RlB55rteeB6UgZeTrDEjG+OdQskwdguTLjuI4lFtmK
7dvVPBgbp7cEx1ug/a3yE+tD+XBt055buiPmKHGWi7pkfJgxHtqdFG6OkZOz
7reIaBBfrenXPiBRXP2GyjxKQ3T70hpXfxJj9/vPeB2jYcB3h/+EH4nJ/rV9
rBwarAQTxhXrScxQJ2dLTtBgmPJUzvUiscpN8yFPSsPWGuk6FpKouantLbtA
wzMX2eXRRSRKulhZTc00rJS7mlw1IrHgbFz0oRYaXE0T8380JPFsksJjXRsN
Vf1m7kv0SbxqIZluU9BQGpPa+qcuiQMhRHT3AxreiA0+lU4RKFBaewwpaehq
ybyb/5RAl9o9nFIVDQ2y5W3BwwSuTO/XbBuhIaRng8pyiEAfgfTS6BgNrMb2
LSceE5gYQ3Fev6aBNH0Zl9tDYNpXv2lqJmnoPWTiFNBFYLrJUE+Smgb9bqku
eY/AkxfPHpma+vxzIyZz2ggs+XVW1LVpGiRpGtOAFgIvbNi2Om2GhgjVxtVk
M4G1/Dt2qz7RcMaAyuppIlA26ajRamlo+ilsIldO4H8sHR7c
      "]]}},
   AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
   Axes->True,
   AxesOrigin->{0, 300000.},
   PlotRange->{{0, 10}, {300000, 900000}},
   PlotRangeClipping->True,
   PlotRangePadding->{
     Scaled[0.02], Automatic}], TraditionalForm]], "Output",
 CellChangeTimes->{{3.5612102544414682`*^9, 3.56121027854406*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 FormBox[
  RowBox[{"Simplify", "[", 
   FractionBox[
    RowBox[{
     SuperscriptBox["B", "\[Prime]",
      MultilineFunction->None], "(", "t", ")"}], 
    RowBox[{"B", "(", "t", ")"}]], "]"}], TraditionalForm]], "Input"],

Cell[BoxData[
 FormBox[
  FractionBox[
   RowBox[{
    RowBox[{"500.`", " ", 
     SuperscriptBox["t", "1.5`"]}], "-", 
    RowBox[{"15000.000000000002`", " ", 
     SuperscriptBox["t", "0.5`"]}], "-", 
    RowBox[{"250.`", " ", "t"}], "-", "35000.`"}], 
   RowBox[{
    RowBox[{"-", 
     RowBox[{"10000.`", " ", 
      SuperscriptBox["t", "1.5`"]}]}], "+", 
    RowBox[{"5000.`", " ", "t"}], "+", "800000.`"}]], 
  TraditionalForm]], "Output",
 CellChangeTimes->{{3.5612102545039144`*^9, 3.561210278622063*^9}}]
}, Open  ]],

Cell["\<\
Observese que la tasa proporcional de variacion del beneficio  tambien \
disminuye\
\>", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"B", "'"}], "[", "t", "]"}], "/", 
    RowBox[{"B", "[", "t", "]"}]}], ",", " ", 
   RowBox[{"{", 
    RowBox[{"t", ",", " ", "0", ",", " ", "10"}], "}"}], ",", " ", 
   RowBox[{"PlotRange", "\[Rule]", " ", 
    RowBox[{"{", 
     RowBox[{"0", ",", " ", 
      RowBox[{"-", "0.15"}]}], "}"}]}]}], "]"}]], "Input"],

Cell[BoxData[
 FormBox[
  GraphicsBox[{{}, {}, 
    {Hue[0.67, 0.6, 0.6], LineBox[CompressedData["
1:eJwVjnk41PsegMmSbNeSImL4OclYSu6SDr7fQ7JGWepcObrmYAhJRYu6yZI9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      "]]}},
   AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
   Axes->True,
   AxesOrigin->{0, 0},
   PlotRange->{{0, 10}, {0, -0.15}},
   PlotRangeClipping->True,
   PlotRangePadding->{
     Scaled[0.02], Automatic}], TraditionalForm]], "Output",
 CellChangeTimes->{{3.561210254566267*^9, 3.5612102786688576`*^9}}]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell["\<\
Ejemplo 2.- Evoluci\[OAcute]n ciclica del precio de un producto estacional\
\>", "Subsection",
 CellChangeTimes->{{3.5620446618496323`*^9, 3.5620446914414206`*^9}, {
  3.5620449107294846`*^9, 3.56204491160165*^9}}],

Cell[TextData[{
 "El precio de las fresas, ",
 Cell[BoxData[
  FormBox["p", TraditionalForm]]],
 ", en \[Euro]/kg, varia ciclicamente (es un producto estacional), supongamos \
que se puede aproximar (",
 Cell[BoxData[
  FormBox["t", TraditionalForm]]],
 " en semanas)"
}], "Text",
 CellChangeTimes->{{3.562044695225949*^9, 3.562044705522222*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"p", "[", "t_", "]"}], ":=", " ", 
  RowBox[{"1.2", " ", "+", " ", 
   RowBox[{"0.6", " ", 
    RowBox[{"Cos", "[", 
     RowBox[{
      FractionBox["6", "52"], "t"}], "]"}]}]}]}]], "Input"],

Cell[TextData[{
 "En una cadena de alimentacion se ha observado que su demanda, ",
 Cell[BoxData[
  FormBox["x", TraditionalForm]]],
 ", en kg,  depende del precio, p, , en \[Euro]/kg, de acuerdo a la expresion:"
}], "Text"],

Cell[BoxData[
 RowBox[{
  RowBox[{"x", "[", "p_", "]"}], ":=", " ", 
  RowBox[{"5000", " ", "-", " ", 
   RowBox[{"1200", " ", "p", " "}]}]}]], "Input"],

Cell["\<\
\[DownQuestion]Cual es la tasa de variaci\[OAcute]n semanal de la demanda?\
\>", "Text",
 CellChangeTimes->{3.5625901626505046`*^9}],

Cell[BoxData[
 RowBox[{
  FractionBox["dx", "dt"], "=", 
  RowBox[{
   FractionBox["dx", "dp"], " ", 
   FractionBox["dp", "dt"]}]}]], "Text"],

Cell[CellGroupData[{

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{"\[PartialD]", 
     RowBox[{"x", "(", "p", ")"}]}], 
    RowBox[{"\[PartialD]", "p"}],
    MultilineFunction->None], 
   FractionBox[
    RowBox[{"\[PartialD]", 
     RowBox[{"p", "(", "t", ")"}]}], 
    RowBox[{"\[PartialD]", "t"}],
    MultilineFunction->None]}], TraditionalForm]], "Input"],

Cell[BoxData[
 FormBox[
  RowBox[{"83.07692307692308`", " ", 
   RowBox[{"sin", "(", 
    FractionBox[
     RowBox[{"3", " ", "t"}], "26"], ")"}]}], TraditionalForm]], "Output",
 CellChangeTimes->{3.561210278871666*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{"%", ",", " ", 
   RowBox[{"{", 
    RowBox[{"t", ",", "0", ",", " ", "52"}], "}"}]}], "]"}]], "Input"],

Cell[BoxData[
 FormBox[
  GraphicsBox[{{}, {}, 
    {Hue[0.67, 0.6, 0.6], LineBox[CompressedData["
1:eJwV13k8VN8bB3BbQlpshUr2ZWbIln15zNwZRtaZS/YtbZJEliIpSqVISSWF
L6JosYSITpKSyJYU0kqLLWVL9Du/v+b1fp2Ze+8553k+545CwF7ONj4eHp4y
Xh6e/3/ad56+OdJaahGzQ37tbpcvFvtdpZKXuJy1ZFcuW9+a9tjSg9ds/AOZ
Y7lXz4mVk9Zl2erqqNBO3rVcbRNodTTtk2USr7vJUxJZSsR87SXTfll+7hlo
aiDbLUNP6KY0nuWHc1byZxD53lL7dLtKRooEfIu0Cn1ITljuQ8hu+JgSXJIu
TzkvwAselcpxQxv1wTRbY/6yjTDQy+3K3+eYw1iulWZq6SoI907wXWXOgEcz
PuW1q6XgN6NNx6TOGsiAkMQObRkQHOj1fH1pM+x0Givu+G89EDWnNbW3OILX
6rAiVsV60PAMuTYU6AhO/VP5tU/WQ68kR+ZCmCMY71y4WvB1PSwaWm14e8YR
ROJFzx7QkgNqmMwygUZHuHWHsl+hRg40eNfrBq1xgskVO8z2dWyArEB4rnbY
CeqH9m4X4lEAn8JumwUrZ/h4y7qKJqQAYZ5lP3ZaO8OSiA1CzqsUYGPVhfp2
O2ew439547K8AqSNF42nb3GGvg1aoxQrBUD+Hd7jwc4w6zYSbn9UAbYS+7b+
yHAGvZadR84JKMKVsa8is8PO4HoOOitFFYGb7Lt3eMQZDrpLK/VJKoKJtNtg
509naBh+2qikogg1ntEDV+edwUlATegeUxF8J631BVZyIMT8S8rr44oQUXXR
W2wTB4ru+GetE1YCms2cm2ocB7q2DD2aEFOCr3ahd34f5cDiv6DhRlklyLwQ
blSfxAGu037dPTQlCN6pPkBPw+MTx5/VOSpBqn6Xg3g+Htct+e2ToQQeUace
P3uGxyum7XKVlEFz/kxV8gouqHvHhEXQlCFA4N3KenEucJfwXGJvwi4Ojvix
mgtFLsKffrKUYcr951bDDXh8eu0BepAyrBk/e/f8RjxuaFXw6a4yvKjXWOft
iMdrkhdULFTgq1OHPC0Zj7OuT21lqcDH1XFnjqRw4W8nGs11UIE/pGZKZxoX
8n9MDaz3VYFq33SbHZe48HudX71UvArwtzSe9izgQsZh/cNLGlSgJ+HPnZB6
LvQSAzxfmKpAuk7Fm4xygdYxM6vooAqCvbHLeSe4EO8t/tPPVRW8/OfXPJ7E
84u0/tC/XRU28PnlG89y4UBh6aPuJFX48SHt5AQfCbIix482NqvCyx7mv8Q1
JHi/1BLIt1eDq4e1rxDmJLRbmB2sdlEDdT69shBLEui32RMvvNVANnEwIN2K
BNUzgf1Te9TAuNw9tZNJwphtZoV1ihq8SllcKutAQnzTkm0/2tTgQuIZyVfe
JExukuj716MGqz/anq32JSGwQN5ZclANotbdvnbRnwSbRFNz83E1oNU27bPZ
RoIYfZ9U6kp16DgrO7Q/mIT/6vqf6Dqpw79bzNLZAyRIan43tXZThx2Nd9Uv
xJBwPGum1NNPHbb2lNM0D5EQFCN+LTFUHRZB/o1jPAl6xjaRPWfVgby1rsb3
OAmNFeWqBzvUIS5YhbyRRoKB8qOslDfqcICTvWfxHAlF59vE8z6oQ83nzBWO
6SScCfu22PJTHQL3/vryMYMEV+0Nr9eLa4CB/o6P3VdIGC4+lfSIowEbLcNf
f8gnwe8v0XnMUwM8PvrML7lOwlu7f+tsAzWAwpB6rVxIwovR8LLOCA34LFZf
wblBwt2N3gOfLmlAwVYH3r23SNCIX6NelKsBAv+6+3bexvNv7wgLvqkBdWq8
wd53SLiwjyU0VasBgubOJQalJBws36gnOKgBLcIO129UkPCL//uh58MasIQS
oXbgHgnBZP6zlAkNmGSEezEqSfCZkvZZw0cB417VD0+rSHjN7CrqE6FA1Xi0
9tFqEpwyzvzKlqAA27RP1/A+CQxDvpPqKhToOyftlFZDwoOkB10jmhT4Lnkl
yKAWr19vpFypAQUsqmINe7DVD/woN7ahwEP92uEldSSI1na/s91NAbVZ3msq
D0k4tixVY+V+Clz+6GSdg73oyd7fFUsB1aGBXClEws+/dcJeKRQoPmwaNIEd
ZB9Nyl+kgKlc92uXRyR8vqqb/TmbAtRhk+l72D0Whfp7SinwbE6Mub2BBMdU
/8M6Nfj6Gi4RldjPBtc+n2qggKyTqCvvYxKstHska1rw95nKwyzsmvizvnHd
FBi1SFZPwtbrsL1JH6BAfou2bAN2icKSKcEhCgy+XvJgBls17KFlyxgFdhf/
Xa7eSEJ2w4FTqTMUGP8mtIqLLS2h/4rLQ4XZcxsaorHPbR3bIC1MhUleQ+XL
2MsqioL6xaigM8YyqMBOFNh6L0eWChNBNrPN2Avkep5tSlRwHd4U9BY7suC1
rQaNCuFay05/wR6fSrswqk8F5o4n3j+wd7Ls3peaU+Ge5NbB//tDhiA1kkWF
LKnPq4axPYZRhIkjFVA+e7Ifu9swBi1uoUKHW0ZCK7b9iU3LHvtRYZ9yW2M1
dlPvuEvSLipouE7fu4YNGjdzNodRYe8lqS2Hse8fCPyxMoYK137qFXlg6z6X
M+hOoMLfxx43tLFfLYZw+U5TYff2kDsC2NF6D0O106ngKHpCqhuvn+zOlSk+
WVSoPFHWdw27Lsu3+HQ+Fdwq53i3Yft13HlWU4KfPyrohCo2nyDP0NcKKqRX
iu/9hPfTZm+OPPMJFdbGsrwdsb/nTZiHt1Lh39/JwEVcD2d6wTP3FRUMJ6Rb
i7A7rT5cWPhChdEIuYfjuJ4iInXKqWNUOGSpxj6NLV18pN19mgqx3+b1lLG9
JRWXVQrS4En2dhoL1ycPO0z98woa2G3QMmmvx/14qIEpvoYGd7cp33DB/joU
EB+iRoOow8uKObjew+7nTana0CB7JS9dCveD1NgvcRcnGvjW7Pc6iPunWpHQ
TnCjwWqvFW/e4v5aSP4cNLiTBh3X6XNncP+d8FF5f/EkDWh9nW8e4P6lnI9Y
eJJGg6TT54QXcH+3Pn0i+/syDR7plmYZYYvrbHdxukkDq4Da0dwyEq7yFz4X
aqHB5lFRMMd5AUYzwwZdNDhc0ZTqhvPkY7D1km19NOineBD/zxv1nmHLRz9o
UMc72J9STEJZkfq9A6KaoN/m2JGB88plILqzUFITlF0f2p/BeTYr1jz+ap0m
dI01ah8uIME8ZhdFV1MT7s4nUF3ycL/Z38z+bq8JujHX/zRfI2FgknrKM1UT
/Mh449c4T48LacQaX9KEAMuZtB3nSdCWUw1Zk6sJuzi8JyZxHiey5TldZZoQ
3u3qMJuC558jKbu5RxOm/ZY7Pj6B68l+4YbJei0QMYo6tAXnv+LWP1ekVbVA
Rm9mMA2fDy+iZ85Ma2lBlHjrUFMUCRvyf+4rAy1YT3p9kt+P6/vPF2NKoBaQ
+okF6fh8kShqa5Yp1oL/Lu2uj/HC+VbXUjtTrgXnhq7n+nmQsL3r2a1XD7Tg
MvLXATecF4sNaWltWjASkOY2zsX16lLlLjypBSlbn7xavpmE23w532aNNkJA
SfRKOyMS2N77hHubNkJOUvbXjhUkrHL1P3D65UZY6G87JStKQq+D8zfo3QiF
gflyPsK4n0Gn+ca3jSAyskSuh5+Ex2nRjeaC2mDgxkw9ic/zj/uNEldqaEP8
7an+xfdc2GBazV8eog1N2v/tU7/NhaOGd02Xh2uDUllYVftNLgzpFYXviNIG
lfawpfsLuXCbdunT2nht4N29o7k4hwsWctGPE9O0IaZda3TwHBe8eI0SXCu0
oUK+PNozkguZT6v4/sxpgwRvrsB1Yy6IV/5REl7UBoXHeeVTm7iQnG/OlObT
gRjht1QrXS7EHnmcZCCiA59cFGNaKFzwNX0pGi6rA5q8ciW31nJB+c7Q6hET
HSgqKhS/8ZcDtzKkqO9idOB+hcPckVoOoG3h3IYFHXhpzu8/TuPAg0ZRXw0+
Xehw1RTpVONAtdL1oLOCurAY95f/riIH7n7oPeKzUhcKEl6PeUtzINfb4u4f
eV3oy/zYdISfA0ddhJfrEbqQluR053uvMzCY2U15p3SBp9NBenO8MzQptxgf
W6MH/v0n+i8+coK/OwfDjsrpQ/SEj86crwOIt6VaHTTdBFKJyxZexdnCt4ys
NiuuAQjpR2rP0Fkw/nnbbYabIZhdH33yZsEKergtShBuBPJc/cfxFBMYtR79
ERljDPa9g+kTWdrQmL077FCcCSiVTtY2i6+DGOnjKXEXTeGziLypz+9lKGC1
98L9q2ZwUPmcwccECtLY1M47cd8cyl9qbaPnGKK7VdmNU+0WsEb5tsmfSkA7
HlLfbnplCSVSQ9R3okz079cNenUUQEiOsBMnmI0+2WY9CpsHfH7v6K9TtEeF
XQ82XIi1Ardnf62ttZ2QaIrftSdxVnA+7oxyr4ETCrURWD8dbwXubrEDgeZO
yKRus+yWY1Yg5/9kYJ+tE2q7/lZSJsUKck5HfnMPdEK/D8wKX822glR2wAO/
i07ISl7/d36DFYT6mvFa/HFCfcHFzyqE6MAkqlXelzkj25zftQ9F6GC8tRQt
VDmjmi7zO89F6SCZVrB7TZ0zumTSfuH9Kjoc8pwZsXjqjEihqQBRGToIZdQe
8ulzRm15FgtbNehQQBx5946Pgx697dCRsKWD4ipP3gEHDtJesVZFzo4OrxUK
Dh7kclCOVaC0hgMdlqV7fZBw46C4oulFCw4dZoYXwkz8Ocgkcu2LIA86OBsV
nHIN56AKsW3bG4LowBh0L27O4KBCm9nMfcl00Fz97336Ww5yqwhOKDpDh956
HnnBQQ4Skv+wezCVDtukPPeFfeKgoJlmM/t0OuSaxbLMRjhI6/qVd+pX6SD2
YFdm+gIHVfJbKr6/TYdf83Mjrhu46En9sRsOnXT45hmRK+vLRZGUP2nHuulg
uaVm6UgAF6lmhBx80EOHXe1fvKu3c9GJPVs2U/rocLp77pVVCBfZrdMYXfKZ
Dmsj896sOcRF3QdeaNdN0WGirGHLy8tc9Elfopoqw4B5B5/abS+56JqMppT5
Wgak5vGle3dykcciK8xhPQNC2jW+Ob3iovanB2n7FBjw8oGzIKWPi+o9PuZU
ajBAvzF6rmCIiy7Fl560MmHASKaobuNfLuJuaxnimDEguepwYvg/Llph+4UR
aMGA0DAdthwfiY5JyCwepzMgYPiT6valJAq7Hh/2wpYB9qONig/FSGT/wtFz
iycDSh98uHxBhURCpbuqd3ozoK8zr3lejUSNFxKkDvoyoOPBrgBvColMfKte
Zm1lQFBvzwvxjSRSn5QjPu5mwA53diTLiER80mO0PbEMaH59qbCdTaKqracX
j15lAKfCee2eXfj3vErzJ7MZ4FO/3sNgN4keXLs/czaXAQf5u+Xng0nU8GZo
4loBAyK7womoUBK1OVp9qrnFAKeg4TfGUST6bDr9dLKOAZVHREeGE0i0483p
xrmH+PudtEO7jpHoe6TSI54GBgz5xJwdOk6i8VKnmhVNDIg57mrWdZJEf9SK
SyhtDPhyXSknMpVEYpJ+aQHvGHC404b8cplE6aXTZ3a9Z8BluucnuSskWu14
5lToRwaMne8b52aRaN2pmoS4IQb0MKXj717D8+eRiswcY4CEikekXh6Jiq8W
h+VO4P3+XfLNJp9EWqb0vUWTDJCiBfe6F5BIL3LvzsppBni+tVILKSSRxUiz
R+ciHh/6l+BXTKJHJ/22vOEhoLUs8IVzCYkItRnuez4Cgu+Fp1jcIhE7QNl+
TJCADvGGOJE7JCJ74yxFVhKQX1AuElxGotcRUmZiYgRk3ZyWNS4nkYdEiZG0
BAGpUv55vBUk8nN4o6O6hgC55IW1x+6RaHejnjJ9AwG18U2FLtUk0s6ckopQ
IKAzcF+y6H0S/d5btbRIiYC9dTPS9dhxa01/LFcnoM36g7ZYLYnoP//2A4UA
HrXRmjLspU/r28JpBNx7pTLm8IBEZ8PoZW+0CRBdF+cYVYef10YgX1SPgBk/
50P89SSSkWu6YLmJgOXt1dxT2P81sw8UGBOQWFQzl/SQRNuzl+3uNSWAjiSa
F7GpEa1eyywImPSJg1BEogp5Z9hHJyDzrqQa4xGJoqfFdfMJfD9JkYx8bPMX
3UqvWQRE+uaX8DTg+vwvQ0qETcBsX0vQFuymKLel5psJ/P4S1F6Efcpedm6v
PQEtIUEDv7Edlfq//+dIQMRcdZrpYxJJzl3tf+VMwM+rjNFY7N423zYhkoDz
SXPj1dhZ+QrI1JUAXXrL5XFs/4OfSkPcCFCvufldvpFEqk4FebkeBHDNkj/a
YX9X2XGh2wvvR6T/kXDsO/PqSUt9CYiPUHqajr2/43u0iT8BfDeeld/FNios
CdqzFe/XINv6KfZCbIhXzjYCPNm5R3qxGzjaDl07CFCIfB7wGfu4+qSlYBAB
310bvn/H3rxYrmMcTICSeZLMCPaq7gil4BACet5Kj+P/K6j7hqFUdigB/9Gj
d7/Dvnx4TrAzjICHw4UpL7F9XGpnBSII+Hu12K0WW5F66LthFAEPLp9ozsUe
4rHsDzpAwNxe5oej2MU9PG1XYwgwX/092wc7tKThYfshAq5/PLxkE7b+0cRS
/ngCBpPFxAWxZ7ew8gyOErBeo/hJB16/Ok2hC7sS8Xx0PeQvYR/lf3486zgB
Woc1Fd2xWW+So1+eIGAZe1OLJLbIHfsgvmR8f/WEtS14/14mrvTadIaACmmK
RCy2m/Z5yytpeP0mXs224vpYJ+ii03aegBu3lw6HYH/oW63Em0FAjtpIrAh2
UFKm4I5MAsRkDXJ0cL1peXvNXs4iYFVwl2YdrsdfunLfX1wjQIpyfisDO/Zd
bqtuHgGa9bNPLXE9p266kb5YjNd3nUL0LO4Pn8RV88tu4/qSbBEPxKZ1RfnL
3CWg6f64YEsNiZ6HsrT0KwhQ2an39xTuN8GST093PSDAcXOhXFcliV79sdWK
qifgGkfxpAx2PrssPRER4P3O2sET9zN9ON4/u5EAbXOLb+24/+MU5ea7X+D6
Pt64PfEuzvt9x/w/thGw2BldXIDzYx0aeTreTsAlTVu7htskqvGuTRd5RYCw
jFjeKM6f6UtuWjBAwKZdS4pFb5Boz8rz/sWjBPyKuOYanEMiM58/T6vHCVjq
x4liZOP1v+Wv1fQT17NG+4wUzsciW+3591MEGAwbydzCefr5WGv66kUCfq/c
/iUvg0Ref5c+O7KCCW7JrZ/Kk3F/b96rlbqKCZuPrVGyOoXz+nJPepY4E9Rb
PzQ1nyDRJcMC/6rVTHCRZZu34rzvDqPPj8gx4Yrdm7Gsw7i+v8VquW1kQsSf
NRW+Yfj6oStPpekwYalaBn8cPk+CZ3K/PNdjgsnV+omMEBKlLHmaZW7EhB9C
Yterg0jUriC2TMmKCa3F65NrA0jk6lEwPMphwrYrJysfOuPz5oMhQ82FCZlv
v2044YjzZufza35bmHBQKm/jZnvcL5HjLl2eTEi7eIh4ZEOi/nPGjdWBTPBx
v0XuscR50NKakxDJBJbbrswnVHwec/z+Pohmgu0zarmRBq7vN5Nbpg8yobnI
J/a6Kt7f4TUrdx1mgmzJC8UwBdxf/AGHHE4wYeiCdFfzajwfs2l3mUwmUJsP
+sXwkCjqlpzEnTomiNg92juC3zecRjVXvHvIBNUeCcGmF1ykrmkuvLyBCfJq
uy9kNnNRb4nnv6AmJlTH+/+n/5iLjEou/VB9yYRaKus0rZKL/twUb7z2ngmW
rz970K5w0aEiwYgUfhaI1Bcu7PPnItevUqF1S1hAWnl4lXhzkZa6yu6RpSwI
XWS1f3DnoneFDH9bURZslbk5b87hIovCeHtBKRZUW7+JqaVzEc/1Pypxqiz8
v4Sf54UiFyXkjfXsYbNg5/l6ti1+v9vulceK2syCK/zvKvX7OMhGyq0y3p4F
ihIRc7KvOWhF0qML551ZUHjvJl9fGwddCkon77uzwE/ghYVGPQeV6Jh0CgSx
oHR7kea/Kxz06uGx1iunWJB4/9b5iyQHqfWva2xuYcGE89vPZfedkV3rX/V/
rSxQ8ESWtApnFFrff0a/nQVRHE/e3NvOqDona0t2Nwsefw2vj83D79Pb1v3Y
P8ACTmyrzcJpZxQ8tlZcfpwF905NDSn5OqMynrV+keLWcLn1eKsYjzMyU5H5
q+huDZGyivrP9J3Q17vh3jID1jDemRNTLGOP9of8vRrlYwOjLzzGVfez0T4z
rkbXdxs4Wi73unAtEwnaC71r2cOGZmI4nv4Q0Gxq8G3JUDacNF8UNygG9KOz
Pc47jA1TNzX4VS4Cane7vGE8kg3u3cslp0IAZQZS/MXj2eDpfTTdRw7Qxli7
z27n2BBkNjReNWuB3IrPfv9SyYZfXsapjkFmyHbsd43WfTYsaS8SULYyQ+Y6
7slRtWxQIYeyJ9aYIcUqBZowYsN0V2ZE2BNTNNpQtofWjO27fFBG3hQdfds9
EdbHBtt29RrebmO0f73xo9oBNvjdpIx73zRGO/yupgm8Z0OSD42vPN4Y2Q1t
0834zAamdcKEtaYxWj05HX5/lA1bOEZ6cseNkNAmT4Jvgg3hFp+z6F5GaD7q
oeTmSTZUBQVZ+ekaofcLSff6p9mwYT5jV9I7Q9QFI8dU5thQ/PiUQFqFIWpK
cHINmWfDi5RfQumnDFF1U4Vq1QIb/hXFHj3rZ4iKhWVm/v1jg552V+xxA0P0
Pzk+ddk=
      "]]}},
   AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
   Axes->True,
   AxesOrigin->{0, 0},
   PlotRange->{{0, 52}, {-83.07691038329044, 83.07689652133816}},
   PlotRangeClipping->True,
   PlotRangePadding->{
     Scaled[0.02], 
     Scaled[0.02]}], TraditionalForm]], "Output",
 CellChangeTimes->{3.561210278949667*^9}]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell["\<\
Ejemplo 3.- Inversi\[OAcute]n publica y crecimiento en el modelo keneysiano\
\>", "Subsection",
 CellChangeTimes->{{3.5620449076650915`*^9, 3.5620449882414045`*^9}}],

Cell[TextData[{
 "En la teoria keneysiana se supone que el gasto total ",
 Cell[BoxData[
  FormBox["G", TraditionalForm]]],
 " de consumo de bienes y servicios es una funci\[OAcute]n del producto \
nacional bruto ",
 Cell[BoxData[
  FormBox["Y", TraditionalForm]]],
 ", que se representa por: "
}], "Text",
 CellChangeTimes->{{3.562044963746269*^9, 3.5620449654265327`*^9}}],

Cell[TextData[{
 "(3.1)\t\t",
 Cell[BoxData[
  FormBox[
   RowBox[{"G", "=", " ", 
    RowBox[{"f", "(", "Y", ")"}]}], TraditionalForm]]]
}], "Text"],

Cell[TextData[{
 "En muchos modelos se supone que la funci\[OAcute]n consumo",
 Cell[BoxData[
  FormBox[
   RowBox[{" ", 
    RowBox[{"f", "(", "Y", ")"}], " "}], TraditionalForm]]],
 "es lineal, esto es"
}], "Text"],

Cell[TextData[{
 "(3.2)\t\t",
 Cell[BoxData[
  FormBox[
   RowBox[{" ", 
    RowBox[{
     RowBox[{"f", "(", "Y", ")"}], " ", "=", " ", 
     RowBox[{"a", " ", "+", " ", 
      RowBox[{"b", " ", "Y"}]}]}]}], TraditionalForm]]]
}], "Text"],

Cell[TextData[{
 "Si ",
 Cell[BoxData[
  FormBox["G", TraditionalForm]]],
 " e ",
 Cell[BoxData[
  FormBox["Y", TraditionalForm]]],
 " se miden en millones de dolares ",
 Cell[BoxData[
  FormBox["b", TraditionalForm]]],
 " nos dice cuanto aumenta el consumo ",
 Cell[BoxData[
  FormBox["G", TraditionalForm]]],
 " si el producto nacional ",
 Cell[BoxData[
  FormBox["Y", TraditionalForm]]],
 " aumenta en 1 mill\[OAcute]n de d\[OAcute]lares "
}], "Text"],

Cell["\<\
En un estudio se comprob\[OAcute] que para EE.UU. \
\>", "Text"],

Cell[TextData[{
 "(3.3)\t\t",
 Cell[BoxData[
  FormBox[
   RowBox[{" ", 
    RowBox[{
     RowBox[{"f", "(", "Y", ")"}], " ", "=", " ", 
     RowBox[{"95.05", " ", "+", " ", 
      RowBox[{"0.712", " ", "Y"}]}]}]}], TraditionalForm]]]
}], "Text"],

Cell["\<\
Consideremos el siguiente modelo macroecon\[OAcute]mico para determinar la \
renta nacional (o producto nacional)\
\>", "Text"],

Cell[TextData[{
 "(3.4)\t\t",
 Cell[BoxData[
  FormBox[
   RowBox[{"Y", " ", "=", " ", 
    RowBox[{"G", " ", "+", " ", "I"}]}], TraditionalForm]]]
}], "Text"],

Cell[TextData[{
 "a) Hallar la variaci\[OAcute]n ",
 Cell[BoxData[
  FormBox["\[CapitalDelta]Y", TraditionalForm]]],
 " si ",
 Cell[BoxData[
  FormBox[
   RowBox[{"I", " "}], TraditionalForm]]],
 "cambia ",
 Cell[BoxData[
  FormBox["\[CapitalDelta]I", TraditionalForm]]],
 " uds."
}], "Text"],

Cell[TextData[{
 "\t",
 Cell[BoxData[
  FormBox[
   RowBox[{"Y", " ", "=", " ", 
    RowBox[{"95.05", " ", "+", " ", 
     RowBox[{"0.712", " ", "Y"}], " ", "+", " ", "I"}]}], TraditionalForm]]],
 ", despejando Y se tiene"
}], "Text"],

Cell[TextData[{
 "\t",
 Cell[BoxData[
  FormBox[
   RowBox[{"Y", " ", "=", " ", 
    RowBox[{
     RowBox[{"3.47", " ", "I"}], " ", "+", " ", "330.03"}]}], 
   TraditionalForm]]],
 " incrementamos Y e I en  ",
 Cell[BoxData[
  FormBox[
   RowBox[{"\[CapitalDelta]", " ", "Y"}], TraditionalForm]]],
 " e ",
 Cell[BoxData[
  FormBox[
   RowBox[{"\[CapitalDelta]", " ", "I"}], TraditionalForm]]],
 " "
}], "Text"],

Cell[TextData[{
 "\t",
 Cell[BoxData[
  FormBox[
   RowBox[{
    RowBox[{"Y", " ", "+", 
     RowBox[{"\[CapitalDelta]", " ", "Y"}]}], "=", " ", 
    RowBox[{
     RowBox[{"3.47", " ", 
      RowBox[{"(", 
       RowBox[{"I", " ", "+", 
        RowBox[{"\[CapitalDelta]", " ", "I"}]}], ")"}]}], " ", "+", " ", 
     "330.03"}]}], TraditionalForm]]],
 " "
}], "Text"],

Cell["Restando las dos expresiones anteriores se tiene", "Text"],

Cell[TextData[{
 "\t",
 Cell[BoxData[
  FormBox[
   RowBox[{
    RowBox[{"\[CapitalDelta]", " ", "Y"}], "=", " ", 
    RowBox[{"3.47", " ", "\[CapitalDelta]", " ", "I"}]}], TraditionalForm]]],
 " "
}], "Text"],

Cell[TextData[{
 "Si \[CapitalDelta] I varia, p.ej: ",
 Cell[BoxData[
  FormBox[
   SuperscriptBox["10", "9"], TraditionalForm]]],
 "$ \[Rule] 3.47 ",
 Cell[BoxData[
  FormBox[
   SuperscriptBox["10", "9"], TraditionalForm]]],
 "$. "
}], "Text"],

Cell[TextData[{
 "b) Hallar la expresion ",
 Cell[BoxData[
  FormBox[
   RowBox[{"dY", "/", "dI"}], TraditionalForm]]]
}], "Text"],

Cell["\<\
Substituyendo en (3.4) la expresi\[OAcute]n (3.1)\
\>", "Text"],

Cell[TextData[Cell[BoxData[
 FormBox[
  RowBox[{"Y", " ", "=", " ", 
   RowBox[{
    RowBox[{"f", "(", "Y", ")"}], " ", "+", " ", "I"}]}], 
  TraditionalForm]]]], "Text"],

Cell["Entonces", "Text"],

Cell[BoxData[
 RowBox[{
  FractionBox["dY", "dI"], "=", " ", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{
      RowBox[{"f", "'"}], 
      RowBox[{"(", "Y", ")"}], 
      FractionBox["dY", "dI"]}], "+", "1"}], "  ", "\[Rule]", " ", 
    FractionBox["dY", "dI"]}], "=", " ", 
   FractionBox["1", 
    RowBox[{"1", "-", 
     RowBox[{
      RowBox[{"f", "'"}], 
      RowBox[{"(", "Y", ")"}]}]}]]}]}]], "Text"],

Cell[TextData[{
 "En  (3.3)  ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    RowBox[{"f", "'"}], 
    RowBox[{"(", "Y", ")"}], " "}], TraditionalForm]]],
 "= 0.712 y de aqu\[IAcute] "
}], "Text"],

Cell[BoxData[
 RowBox[{
  FractionBox["dY", "dI"], "=", "  ", 
  RowBox[{
   FractionBox["1", 
    RowBox[{"1", "+", "0.712"}]], "=", " ", "3.47"}]}]], "Text"],

Cell[TextData[{
 "Habitualmente (empiricamente ",
 Cell[BoxData[
  FormBox[
   RowBox[{"0", "<", "b", "<", "1"}], TraditionalForm]]],
 ") ",
 Cell[BoxData[Cell["0<f'(Y)<1"]]],
 " \[Rule] ",
 Cell[BoxData[
  FormBox[Cell["dY/dI >1"], TraditionalForm]]]
}], "Text"],

Cell["\<\
Esto lleva a una importante conclusi\[OAcute]n para este modelo (es decir: es \
valida para lo supuestos del modelo no de forma general): Un aumento en la \
inversi\[OAcute]n publica de 1% normalmente conllevar\[AAcute] un aumento \
proporcionalmente mayor del 1% en  el Producto Nacional Bruto\
\>", "Text",
 CellChangeTimes->{{3.5620447474016504`*^9, 3.5620449010102406`*^9}}],

Cell[CellGroupData[{

Cell[TextData[{
 "Hallar la derivada segunda de Y para ",
 Cell[BoxData[
  FormBox[
   RowBox[{"Y", " ", "=", 
    RowBox[{
     RowBox[{"f", "(", "Y", ")"}], "+", "I"}]}], TraditionalForm]]]
}], "Subsubsection"],

Cell[BoxData[
 RowBox[{" ", 
  RowBox[{
   FractionBox["dY", "dI"], "=", " ", 
   RowBox[{
    RowBox[{
     FractionBox["1", 
      RowBox[{"1", "-", 
       RowBox[{
        RowBox[{"f", "'"}], 
        RowBox[{"(", "Y", ")"}]}]}]], "\[Rule]", 
     FractionBox[
      RowBox[{
       SuperscriptBox["d", "2"], "Y"}], 
      SuperscriptBox["dI", "2"]]}], "=", " ", 
    RowBox[{
     RowBox[{"-", "1"}], 
     RowBox[{
      SuperscriptBox[
       RowBox[{"(", 
        RowBox[{"1", "-", 
         RowBox[{
          RowBox[{"f", "'"}], 
          RowBox[{"(", "Y", ")"}]}]}], ")"}], 
       RowBox[{"-", "2"}]], ".", 
      RowBox[{"f", "''"}]}], 
     RowBox[{"(", "Y", ")"}], 
     FractionBox["dY", "dI"]}]}]}]}]], "Text"],

Cell["Adem\[AAcute]s", "Text"],

Cell[TextData[{
 Cell[BoxData[
  FormBox[
   RowBox[{
    RowBox[{
     FractionBox["d", "dI"], 
     RowBox[{"(", 
      RowBox[{"1", "-", 
       RowBox[{
        RowBox[{"f", "'"}], 
        RowBox[{"(", "Y", ")"}]}]}], ")"}]}], "=", " ", 
    RowBox[{"(", 
     RowBox[{"0", "-", 
      RowBox[{
       RowBox[{"f", "'"}], 
       RowBox[{"(", "Y", ")"}]}]}], ")"}]}], TraditionalForm]]],
 Cell[BoxData[
  FormBox[
   FractionBox["dY", "dI"], TraditionalForm]]]
}], "Text"],

Cell[BoxData[
 RowBox[{" ", 
  RowBox[{
   FractionBox[
    RowBox[{
     SuperscriptBox["d", "2"], "Y"}], 
    SuperscriptBox["dI", "2"]], "=", " ", 
   RowBox[{
    RowBox[{
     RowBox[{
      SuperscriptBox[
       RowBox[{"(", 
        RowBox[{"1", "-", 
         RowBox[{
          RowBox[{"f", "'"}], 
          RowBox[{"(", "Y", ")"}]}]}], ")"}], 
       RowBox[{"-", "3"}]], ".", 
      RowBox[{"f", "''"}]}], 
     RowBox[{"(", "Y", ")"}]}], "=", 
    FractionBox[
     RowBox[{
      RowBox[{"f", "''"}], 
      RowBox[{"(", "Y", ")"}]}], 
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{"1", "-", 
        RowBox[{
         RowBox[{"f", "'"}], 
         RowBox[{"(", "Y", ")"}]}]}], ")"}], "3"]]}]}]}]], "Text"]
}, Open  ]],

Cell["Para el modelo anterior: ", "Subsubsection"],

Cell[CellGroupData[{

Cell[TextData[{
 "a) Hallar la diferencial ",
 Cell[BoxData[
  FormBox[
   StyleBox["dY",
    FontSlant->"Italic"], TraditionalForm]]],
 " en t\[EAcute]rminos de ",
 Cell[BoxData[
  FormBox[
   StyleBox["dI",
    FontSlant->"Italic"], TraditionalForm]]]
}], "Subsubsection"],

Cell[TextData[{
 Cell[BoxData[
  FormBox[
   RowBox[{"Y", " ", "=", " ", 
    RowBox[{"G", " ", "+", " ", "I"}]}], TraditionalForm]]],
 "\[Rule]",
 StyleBox["dY= dG + dI",
  FontSlant->"Italic"]
}], "Text"],

Cell[TextData[{
 StyleBox["G = f(Y) \[Rule]dG =f'(Y) dY ",
  FontSlant->"Italic"],
 "que substituimos en ",
 StyleBox["dY",
  FontSlant->"Italic"]
}], "Text"],

Cell[TextData[{
 StyleBox["dY= f'(Y) dY  + dI \[Rule] dY =",
  FontSlant->"Italic"],
 Cell[BoxData[
  FormBox[
   FractionBox["1", 
    RowBox[{"1", "-", 
     RowBox[{
      RowBox[{"f", "'"}], 
      RowBox[{"(", "Y", ")"}]}]}]], TraditionalForm]]],
 StyleBox["dI",
  FontSlant->"Italic"]
}], "Text"]
}, Closed]],

Cell[CellGroupData[{

Cell[TextData[{
 "b) Se supone que el empleo ",
 Cell[BoxData[
  FormBox[
   RowBox[{"N", " ", "=", " ", 
    RowBox[{"g", "(", "Y", ")"}], " "}], TraditionalForm]]],
 ", hallar la diferencial ",
 Cell[BoxData[
  FormBox[
   StyleBox["dN",
    FontSlant->"Italic"], TraditionalForm]]],
 " en t\[EAcute]rminos de ",
 Cell[BoxData[
  FormBox[
   StyleBox["dI",
    FontSlant->"Italic"], TraditionalForm]]]
}], "Subsubsection"],

Cell[TextData[{
 StyleBox["N = g(Y) \[Rule]dN =g'(Y) dY , ",
  FontSlant->"Italic"],
 "como"
}], "Text"],

Cell[TextData[{
 StyleBox[" dY =",
  FontSlant->"Italic"],
 Cell[BoxData[
  FormBox[
   FractionBox["1", 
    RowBox[{"1", "-", 
     RowBox[{
      RowBox[{"f", "'"}], 
      RowBox[{"(", "Y", ")"}]}]}]], TraditionalForm]]],
 StyleBox["dI \[Rule] dN =",
  FontSlant->"Italic"],
 Cell[BoxData[
  FormBox[
   FractionBox[
    RowBox[{
     RowBox[{"g", "'"}], 
     RowBox[{"(", "Y", ")"}]}], 
    RowBox[{"1", "-", 
     RowBox[{
      RowBox[{"f", "'"}], 
      RowBox[{"(", "Y", ")"}]}]}]], TraditionalForm]]],
 StyleBox["dI",
  FontSlant->"Italic"]
}], "Text"],

Cell["\<\
Siempre que g'(Y)>0 y 0<f'(Y)<1, se llega a la conclusi\[OAcute]n de que \
cuando la inversi\[OAcute]n crece tambien crece el empleo.\
\>", "Text"]
}, Closed]]
}, Closed]],

Cell[CellGroupData[{

Cell["Ejemplo 4 Elasticidad", "Subsection"],

Cell[TextData[{
 "Un concepto ampliamente utilizado en ec\[OAcute]nomia es el de elastidad. \
La elasticidad, ",
 StyleBox["El",
  FontSlant->"Italic"],
 ",  de ",
 StyleBox["f",
  FontSlant->"Italic"],
 " con respecto a ",
 StyleBox["x",
  FontSlant->"Italic"],
 "  se define"
}], "Text",
 CellChangeTimes->{{3.561213273288774*^9, 3.561213298841303*^9}},
 FontSize->16],

Cell[TextData[{
 Cell[BoxData[
  FormBox[
   SubscriptBox["El", "x"], TraditionalForm]]],
 Cell[BoxData[
  FormBox[
   RowBox[{"f", "(", "x", ")"}], TraditionalForm]]],
 " = ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    FractionBox["x", 
     RowBox[{"f", "(", "x", ")"}]], 
    RowBox[{"f", "'"}], 
    RowBox[{"(", "x", ")"}]}], TraditionalForm]]]
}], "Text",
 FontSize->16],

Cell[TextData[{
 "Supongamos que la demanda, ",
 StyleBox["Dem",
  FontSlant->"Italic"],
 ", de cierto bien est\[AAcute] dada por la expresi\[OAcute]n: ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    RowBox[{"Dem", "(", "p", ")"}], "=", 
    RowBox[{"8000", 
     SuperscriptBox["p", 
      RowBox[{
       RowBox[{"-", "1.5"}], " "}]]}]}], TraditionalForm]]]
}], "Text",
 CellChangeTimes->{{3.5612132374644628`*^9, 3.5612132454642224`*^9}, {
  3.561213337972717*^9, 3.561213347829095*^9}},
 FontSize->16],

Cell[TextData[{
 "Hallar la elasticidad de  ",
 Cell[BoxData[
  FormBox[
   RowBox[{"Dem", "(", "p", ")"}], TraditionalForm]]]
}], "Text",
 FontSize->16],

Cell[CellGroupData[{

Cell["Sol: ", "Subsubsection",
 FontSize->16],

Cell[BoxData[
 RowBox[{" ", 
  RowBox[{
   FormBox[
    RowBox[{
     RowBox[{"Dem", "[", "p_", "]"}], "=", 
     RowBox[{"8000", 
      SuperscriptBox["p", 
       RowBox[{
        RowBox[{"-", "1.5"}], " "}]]}]}],
    TraditionalForm], ";"}]}]], "Input"],

Cell[TextData[{
 "Aplicamos la definici\[OAcute]n de elasticidad. En nuestro caso ",
 StyleBox["f",
  FontSlant->"Italic"],
 " es la funci\[OAcute]n demanda ",
 StyleBox["dem",
  FontSlant->"Italic"],
 " y ",
 StyleBox["x",
  FontSlant->"Italic"],
 " es el precio ",
 StyleBox["p",
  FontSlant->"Italic"]
}], "Text",
 CellChangeTimes->{{3.561213367256647*^9, 3.5612133862750626`*^9}},
 FontSize->16],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{" ", 
  RowBox[{
   RowBox[{"ElxDem", "[", "p_", "]"}], "=", 
   FormBox[
    RowBox[{
     FractionBox["p", 
      RowBox[{"Dem", "[", "p", "]"}]], " ", 
     RowBox[{
      RowBox[{"Dem", "'"}], "[", "p", "]"}]}],
    TraditionalForm]}]}]], "Input"],

Cell[BoxData[
 FormBox[
  RowBox[{"-", "1.5`"}], TraditionalForm]], "Output",
 CellChangeTimes->{3.5612102790432625`*^9},
 FontSize->16]
}, Open  ]],

Cell["\<\
En este caso la elasticidad es una constante igual a -1.5 y debe \
interpretarse como que un aumento en el precio del 1% implica que la demanda \
cae (pues el signo es -) el 1.5%\
\>", "Text",
 FontSize->16],

Cell["\<\
En el grafico podemos observar como disminuye la demanda cuando aumenta el \
precio entre el 1% y el 10%\
\>", "Text",
 FontSize->16],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{"Dem", "[", "p", "]"}], ",", " ", 
   RowBox[{"{", 
    RowBox[{"p", ",", " ", "1", ",", "10"}], "}"}]}], "]"}]], "Input"],

Cell[BoxData[
 FormBox[
  GraphicsBox[{{}, {}, 
    {Hue[0.67, 0.6, 0.6], LineBox[CompressedData["
1:eJwVjXk41AkDx8cMvUOOKRqN5Pot0j6vDhshft+UVitH2yhZlpRufqPFopCh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      "]]}},
   AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
   Axes->True,
   AxesOrigin->{2., 0},
   PlotRange->{{1, 10}, {0., 4283.087644080723}},
   PlotRangeClipping->True,
   PlotRangePadding->{
     Scaled[0.02], 
     Scaled[0.02]}], TraditionalForm]], "Output",
 CellChangeTimes->{3.561210279183694*^9},
 FontSize->16]
}, Open  ]]
}, Closed]]
}, Closed]],

Cell[CellGroupData[{

Cell["\<\
Ejemplo 5 Elasticidad y derivaci\[OAcute]n logar\[IAcute]tmica\
\>", "Subsection"],

Cell["\<\
En la funci\[OAcute]n demanda del ejercicio anterior tomamos logaritmos \
\>", "Text",
 FontSize->16],

Cell[TextData[Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"ln", " ", "Dem", " ", 
    RowBox[{"(", "p", ")"}]}], " ", "=", " ", 
   RowBox[{
    RowBox[{"ln", " ", "8000"}], " ", "-", " ", 
    RowBox[{"1.5", " ", "p"}]}]}], TraditionalForm]]]], "Text",
 FontSize->16],

Cell["\<\
Nota: la relaci\[OAcute]n anterior se dice que es log-lineal\
\>", "Text",
 FontSize->16],

Cell["\<\
que es la ecuaci\[OAcute]n de una recta de pendiente -1.5. Esto nos permite \
obtener otra forma de calcular la elasticidad que es\
\>", "Text",
 FontSize->16],

Cell[BoxData[
 RowBox[{
  RowBox[{
   SubscriptBox["El", "x"], "Dem", 
   RowBox[{"(", "p", ")"}]}], " ", "=", 
  RowBox[{
   FormBox[
    RowBox[{
     RowBox[{
      FractionBox["p", 
       RowBox[{"Dem", "(", "p", ")"}]], " ", 
      RowBox[{"Dem", "'"}], 
      RowBox[{"(", "p", ")"}]}], " ", "=", " "}],
    TraditionalForm], 
   FractionBox[
    RowBox[{
     StyleBox["d",
      FontSlant->"Italic"], " ", "ln", 
     RowBox[{"(", 
      RowBox[{"Dem", 
       RowBox[{"(", "p", ")"}]}], ")"}]}], 
    RowBox[{
     StyleBox["d",
      FontSlant->"Italic"], " ", "ln", 
     RowBox[{"(", "p", ")"}]}]]}]}]], "Text",
 FontSize->16],

Cell["y en general", "Text",
 FontSize->16],

Cell[BoxData[
 RowBox[{
  RowBox[{
   SubscriptBox["El", "x"], "f", 
   RowBox[{"(", "x", ")"}]}], " ", "=", " ", 
  RowBox[{
   RowBox[{
    FractionBox["x", 
     RowBox[{"f", 
      RowBox[{"(", "x", ")"}]}]], 
    RowBox[{"f", "'"}], 
    RowBox[{"(", "x", ")"}]}], " ", "=", 
   FractionBox[
    RowBox[{" ", 
     RowBox[{
      StyleBox["d",
       FontSlant->"Italic"], 
      StyleBox[" ",
       FontSlant->"Italic"], "ln", " ", "f", 
      RowBox[{"(", "x", ")"}]}]}], 
    RowBox[{
     StyleBox["d",
      FontSlant->"Italic"], " ", "ln", 
     RowBox[{"(", "x", ")"}]}]]}]}]], "Text",
 FontSize->16],

Cell[TextData[{
 "Nota: llamamos",
 Cell[BoxData[
  FormBox[
   RowBox[{" ", 
    RowBox[{"y", " ", "=", " ", 
     RowBox[{"f", "(", "x", ")"}]}]}], TraditionalForm]]],
 " entonces ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    RowBox[{
     SubscriptBox["El", "x"], "y"}], "=", 
    RowBox[{
     RowBox[{
      FractionBox["x", "y"], 
      RowBox[{"y", "'"}]}], " ", "=", 
     RowBox[{
      RowBox[{
       FractionBox["x", "y"], 
       FractionBox[
        RowBox[{"dy", " "}], "dx"]}], "=", " ", 
      RowBox[{
       RowBox[{
        FractionBox["dy", "y"], "/", 
        FractionBox["dx", "x"]}], "=", 
       FractionBox[
        RowBox[{" ", 
         RowBox[{"d", " ", "ln", " ", "y"}]}], 
        RowBox[{"d", " ", "ln", " ", "x"}]]}]}]}]}], TraditionalForm]]]
}], "Text",
 FontSize->16],

Cell["\<\
por tanto, a veces nos sera mas util calcular las elasticidades utilizando \
las derivadas logar\[IAcute]tmicas\
\>", "Text",
 FontSize->16]
}, Closed]]
}, Closed]],

Cell[CellGroupData[{

Cell["REGLA DE L' HOPITAL", "Section"],

Cell[CellGroupData[{

Cell["Teorema reducido", "Subsubsection"],

Cell[TextData[{
 "Si f y g son derivables en",
 Cell[BoxData[
  FormBox[
   RowBox[{"  ", 
    SubscriptBox["x", "0"]}], TraditionalForm]]],
 ", si f(",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "0"], TraditionalForm]]],
 ") =  g(",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "0"], TraditionalForm]]],
 ") = 0 y g'(x) \[NotEqual] 0, entonces"
}], "Text"],

Cell[BoxData[
 RowBox[{
  RowBox[{
   UnderscriptBox["lim", 
    RowBox[{"x", "\[Rule]", 
     SubscriptBox["x", "0"]}]], "\[ThinSpace]", 
   FractionBox[
    RowBox[{"f", 
     RowBox[{"(", "x", ")"}]}], 
    RowBox[{"g", 
     RowBox[{"(", "x", ")"}], " "}]]}], " ", "=", "\[ThinSpace]", 
  FractionBox[
   RowBox[{
    RowBox[{"f", "'"}], 
    RowBox[{"(", "x", ")"}]}], 
   RowBox[{
    RowBox[{"g", "'"}], 
    RowBox[{"(", "x", ")"}], " "}]]}]], "Text"]
}, Open  ]],

Cell[CellGroupData[{

Cell["Ejemplos:", "Subsubsection"],

Cell[BoxData[
 RowBox[{
  RowBox[{
   UnderscriptBox["lim", 
    RowBox[{"x", "\[Rule]", "4"}]], "\[ThinSpace]", 
   FractionBox[
    RowBox[{
     SuperscriptBox["x", "2"], "-", "16"}], 
    RowBox[{
     RowBox[{"4", " ", 
      SqrtBox["x"]}], " ", "-", "8"}]]}], " ", "=", 
  RowBox[{
   RowBox[{"[", 
    FractionBox["0", "0"], "]"}], "=", "\[ThinSpace]", 
   RowBox[{
    FractionBox[
     RowBox[{
      RowBox[{"f", "'"}], 
      RowBox[{"(", "4", ")"}]}], 
     RowBox[{
      RowBox[{"g", "'"}], 
      RowBox[{"(", "4", ")"}], " "}]], "=", "8"}]}]}]], "Text"],

Cell[BoxData[
 RowBox[{
  RowBox[{
   UnderscriptBox["lim", 
    RowBox[{"x", "\[Rule]", "7"}]], "\[ThinSpace]", 
   FractionBox[
    RowBox[{
     RadicalBox[
      RowBox[{"x", "+", "1"}], "3"], "-", 
     SqrtBox[
      RowBox[{"x", "-", "3"}]]}], 
    RowBox[{"x", " ", "-", "7"}]]}], "=", 
  RowBox[{
   RowBox[{"[", 
    FractionBox["0", "0"], "]"}], " ", "=", "\[ThinSpace]", 
   RowBox[{
    FractionBox[
     RowBox[{
      RowBox[{"f", "'"}], 
      RowBox[{"(", "7", ")"}]}], 
     RowBox[{
      RowBox[{"g", "'"}], 
      RowBox[{"(", "7", ")"}], " "}]], "=", 
    RowBox[{"-", 
     FractionBox["1", "6"]}]}]}]}]], "Text"]
}, Open  ]],

Cell[CellGroupData[{

Cell["Teorema completo", "Subsubsection"],

Cell[TextData[{
 "Si f y g son derivables en un intervalo (a, b), centrado en  ",
 Cell[BoxData[
  FormBox[
   SubscriptBox["x", "0"], TraditionalForm]]],
 " -donde necesariamente no tiene que ser derivable- y "
}], "Text"],

Cell[BoxData[
 RowBox[{
  RowBox[{
   UnderscriptBox["lim", 
    RowBox[{"x", "\[Rule]", 
     SubscriptBox["x", "0"]}]], "\[ThinSpace]", 
   FractionBox[
    RowBox[{"f", 
     RowBox[{"(", "x", ")"}]}], 
    RowBox[{"g", 
     RowBox[{"(", "x", ")"}], " "}]]}], " ", "=", 
  RowBox[{"[", 
   FractionBox["0", "0"], "]"}], "\[ThinSpace] "}]], "Text"],

Cell[TextData[{
 "Si g ' (x) \[NotEqual] 0 \[ForAll] x \[NotEqual]",
 Cell[BoxData[
  FormBox[
   RowBox[{" ", 
    SubscriptBox["x", "0"]}], TraditionalForm]]],
 "\[Element] (a, b)  y si"
}], "Text"],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{
    UnderscriptBox["lim", 
     RowBox[{"x", "\[Rule]", 
      SubscriptBox["x", "0"]}]], "\[ThinSpace]", 
    FractionBox[
     RowBox[{
      RowBox[{"f", "'"}], 
      RowBox[{"(", "x", ")"}]}], 
     RowBox[{
      RowBox[{"g", "'"}], 
      RowBox[{"(", "x", ")"}], " "}]]}], "=", " ", 
   RowBox[{"L", " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"L", " ", "finito"}], ",", " ", "\[Infinity]", ",", " ", 
      RowBox[{"-", " ", "\[Infinity]"}]}], ")"}]}]}], ",", " ", 
  "entonces"}]], "Text"],

Cell[BoxData[
 RowBox[{
  RowBox[{
   UnderscriptBox["lim", 
    RowBox[{"x", "\[Rule]", 
     SubscriptBox["x", "0"]}]], "\[ThinSpace]", 
   FractionBox[
    RowBox[{"f", 
     RowBox[{"(", "x", ")"}]}], 
    RowBox[{"g", 
     RowBox[{"(", "x", ")"}], " "}]]}], " ", "=", 
  RowBox[{
   RowBox[{
    UnderscriptBox["lim", 
     RowBox[{"x", "\[Rule]", 
      SubscriptBox["x", "0"]}]], "\[ThinSpace]", 
    FractionBox[
     RowBox[{
      RowBox[{"f", "'"}], 
      RowBox[{"(", "x", ")"}]}], 
     RowBox[{
      RowBox[{"g", "'"}], 
      RowBox[{"(", "x", ")"}], " "}]]}], "=", " ", "L"}]}]], "Text"],

Cell["\<\
Nota: a y b pueden sustituirse por \[PlusMinus] \[Infinity]\
\>", "Text"]
}, Open  ]],

Cell[CellGroupData[{

Cell["Ejemplo:", "Subsubsection"],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{
    UnderscriptBox["lim", 
     RowBox[{"x", "\[Rule]", "\[Infinity]"}]], "\[ThinSpace]", 
    RadicalBox[
     RowBox[{
      SuperscriptBox["x", "5"], "-", 
      SuperscriptBox["x", "4"]}], "5"]}], " ", "-", "x"}], "=", 
  RowBox[{"[", 
   RowBox[{"\[Infinity]", "-", "\[Infinity]"}], "]"}]}]], "Text"],

Cell["\<\
Para aplicar la regla de  L'H\[OHat]pital hemos de transformar la expresi\
\[OAcute]n anterior en la forma 0/0\
\>", "Text"],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RadicalBox[
    RowBox[{
     SuperscriptBox["x", "5"], "-", 
     SuperscriptBox["x", "4"]}], "5"], " ", "-", "x"}], "=", 
  RowBox[{
   RowBox[{
    RadicalBox[
     RowBox[{" ", 
      RowBox[{
       SuperscriptBox["x", "5"], " ", 
       RowBox[{"(", 
        RowBox[{"1", "-", 
         FractionBox["1", "x"]}], ")"}]}]}], "5"], "-", "x"}], "=", " ", 
   RowBox[{
    RowBox[{
     RowBox[{"x", " ", 
      RadicalBox[
       RowBox[{"(", 
        RowBox[{"1", "-", 
         FractionBox["1", "x"]}], ")"}], "5"]}], "-", "x"}], "=", 
    FractionBox[
     RowBox[{" ", 
      RowBox[{
       SuperscriptBox[
        RowBox[{"(", 
         RowBox[{"1", "-", 
          RowBox[{"(", 
           RowBox[{"1", "/", "x"}], ")"}]}], ")"}], 
        RowBox[{"1", "/", "5"}]], "-", "1"}]}], 
     RowBox[{"1", "/", "x"}]]}]}]}]], "Text"],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{
    UnderscriptBox["lim", 
     RowBox[{"x", "\[Rule]", "\[Infinity]"}]], "\[ThinSpace]", 
    RadicalBox[
     RowBox[{
      SuperscriptBox["x", "5"], "-", 
      SuperscriptBox["x", "4"]}], "5"]}], " ", "-", "x"}], "=", 
  RowBox[{
   RowBox[{
    UnderscriptBox["lim", 
     RowBox[{"x", "\[Rule]", "\[Infinity]"}]], 
    FractionBox[
     RowBox[{" ", 
      RowBox[{
       SuperscriptBox[
        RowBox[{"(", 
         RowBox[{"1", "-", 
          RowBox[{"(", 
           RowBox[{"1", "/", "x"}], ")"}]}], ")"}], 
        RowBox[{"1", "/", "5"}]], "-", "1"}]}], 
     RowBox[{"1", "/", "x"}]]}], "=", 
   RowBox[{
    RowBox[{
     RowBox[{"[", 
      FractionBox["0", "0"], "]"}], "\[ThinSpace] ", "==", 
     RowBox[{
      UnderscriptBox["lim", 
       RowBox[{"x", "\[Rule]", "\[Infinity]"}]], "\[ThinSpace]", 
      FractionBox[
       RowBox[{
        RowBox[{"f", "'"}], 
        RowBox[{"(", "x", ")"}]}], 
       RowBox[{
        RowBox[{"g", "'"}], 
        RowBox[{"(", "x", ")"}], " "}]]}]}], "=", " ", 
    RowBox[{
     RowBox[{
      UnderscriptBox["lim", 
       RowBox[{"x", "\[Rule]", "\[Infinity]"}]], " ", 
      RowBox[{"[", 
       RowBox[{
        RowBox[{"-", 
         FractionBox["1", "5"]}], " ", 
        SuperscriptBox[
         RowBox[{"(", 
          RowBox[{"1", "-", 
           RowBox[{"(", 
            RowBox[{"1", "/", "x"}], ")"}]}], ")"}], 
         RowBox[{
          RowBox[{"-", "4"}], "/", "5"}]]}], "]"}]}], "=", 
     RowBox[{"-", 
      FractionBox["1", "5"]}]}]}]}]}]], "Text"]
}, Open  ]]
}, Closed]]
}, Open  ]]
},
WindowToolbars->"EditBar",
WindowSize->{2030, 986},
WindowMargins->{{0, Automatic}, {Automatic, 0}},
PrintingCopies->1,
PrintingPageRange->{Automatic, Automatic},
CommonDefaultFormatTypes->{"Output"->TraditionalForm},
Magnification:>FEPrivate`If[
  FEPrivate`Equal[FEPrivate`$VersionNumber, 6.], 2., 2. Inherited],
FrontEndVersion->"9.0 for Microsoft Windows (64-bit) (January 25, 2013)",
StyleDefinitions->FrontEnd`FileName[{"Creative"}, "NaturalColor.nb", 
  CharacterEncoding -> "WindowsANSI"]
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[1257, 32, 421, 6, 130, "Title"],
Cell[CellGroupData[{
Cell[1703, 42, 582, 13, 60, "ItemParagraph"],
Cell[2288, 57, 281, 5, 60, "ItemParagraph"],
Cell[2572, 64, 625, 8, 60, "ItemParagraph"]
}, Open  ]],
Cell[CellGroupData[{
Cell[3234, 77, 143, 2, 53, "Subsubsection"],
Cell[3380, 81, 1446, 33, 2528, "Text"],
Cell[4829, 116, 450, 11, 1232, "Input",
 InitializationCell->True],
Cell[5282, 129, 703, 16, 1952, "Text"],
Cell[5988, 147, 755, 16, 1952, "Text"],
Cell[6746, 165, 176, 4, 480, "Subitem"],
Cell[6925, 171, 92, 2, 1232, "Input",
 CellID->38138293],
Cell[7020, 175, 146, 1, 480, "Subitem"],
Cell[CellGroupData[{
Cell[7191, 180, 124, 2, 1232, "Input"],
Cell[7318, 184, 100, 2, 1632, "Output"]
}, Open  ]],
Cell[7433, 189, 144, 1, 480, "Subitem"],
Cell[CellGroupData[{
Cell[7602, 194, 136, 3, 1280, "Input"],
Cell[7741, 199, 124, 2, 1632, "Output"]
}, Open  ]],
Cell[7880, 204, 284, 7, 480, "Subitem"],
Cell[8167, 213, 73, 1, 1232, "Input"],
Cell[CellGroupData[{
Cell[8265, 218, 136, 3, 1280, "Input"],
Cell[8404, 223, 124, 3, 1664, "Output"]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[8577, 232, 205, 3, 87, "Section"],
Cell[8785, 237, 1142, 34, 266, "Text"],
Cell[9930, 273, 420, 7, 108, "Subitem"],
Cell[10353, 282, 222, 5, 160, "Input"],
Cell[CellGroupData[{
Cell[10600, 291, 172, 3, 154, "Input"],
Cell[10775, 296, 151, 3, 154, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[10963, 304, 203, 4, 154, "Input"],
Cell[11169, 310, 179, 4, 158, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[11385, 319, 158, 3, 154, "Input"],
Cell[11546, 324, 191, 6, 158, "Output"]
}, Open  ]],
Cell[11752, 333, 294, 9, 138, "Text"],
Cell[12049, 344, 1000, 27, 170, "Text"],
Cell[13052, 373, 301, 6, 110, "Text"],
Cell[13356, 381, 9510, 176, 1522, "Text"],
Cell[22869, 559, 984, 25, 208, "Text"],
Cell[CellGroupData[{
Cell[23878, 588, 799, 17, 6016, "Input"],
Cell[24680, 607, 1862, 40, 522, "Output"]
}, {2}]],
Cell[26554, 650, 285, 8, 118, "Text"],
Cell[26842, 660, 1495, 42, 188, "Text"],
Cell[CellGroupData[{
Cell[28362, 706, 747, 17, 226, "Input"],
Cell[29112, 725, 121, 3, 154, "Output"]
}, Open  ]],
Cell[29248, 731, 1598, 34, 310, "Text"],
Cell[30849, 767, 233, 5, 110, "Text"],
Cell[CellGroupData[{
Cell[31107, 776, 462, 13, 106, "Subsubsection"],
Cell[CellGroupData[{
Cell[31594, 793, 791, 16, 1744, "Input"],
Cell[32388, 811, 195, 5, 1264, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[32620, 821, 872, 16, 1712, "Input"],
Cell[33495, 839, 152, 3, 1232, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[33684, 847, 945, 17, 1776, "Input"],
Cell[34632, 866, 187, 4, 1232, "Output"]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[34868, 876, 142, 3, 74, "Subsubsection"],
Cell[35013, 881, 2742, 71, 400, "MathCaption"],
Cell[CellGroupData[{
Cell[37780, 956, 13297, 327, 453312, "Input"],
Cell[51080, 1285, 6387, 133, 1794, "Output"]
}, {2}]],
Cell[57479, 1421, 761, 20, 72, "Text"],
Cell[58243, 1443, 509, 12, 110, "Text"]
}, Closed]],
Cell[CellGroupData[{
Cell[58789, 1460, 188, 5, 90, "Subsubsection"],
Cell[58980, 1467, 454, 9, 242, "Text"],
Cell[59437, 1478, 1247, 43, 134, "Text"]
}, Closed]]
}, Closed]],
Cell[CellGroupData[{
Cell[60733, 1527, 86, 3, 81, "Section"],
Cell[60822, 1532, 583, 10, 176, "Text"],
Cell[CellGroupData[{
Cell[61430, 1546, 192, 3, 122, "Subsubsection"],
Cell[61625, 1551, 26843, 445, 1568, "Text"],
Cell[88471, 1998, 275, 5, 110, "Text"],
Cell[88749, 2005, 179, 2, 60, "Subitem"],
Cell[88931, 2009, 272, 6, 154, "Input"],
Cell[CellGroupData[{
Cell[89228, 2019, 140, 3, 154, "Input"],
Cell[89371, 2024, 213, 6, 154, "Output"]
}, Open  ]],
Cell[89599, 2033, 198, 5, 154, "Input"],
Cell[CellGroupData[{
Cell[89822, 2042, 195, 4, 154, "Input"],
Cell[90020, 2048, 195, 5, 158, "Output"]
}, Open  ]],
Cell[90230, 2056, 206, 5, 154, "Input"],
Cell[CellGroupData[{
Cell[90461, 2065, 142, 3, 154, "Input"],
Cell[90606, 2070, 130, 3, 154, "Output"]
}, Open  ]],
Cell[90751, 2076, 266, 6, 154, "Input"],
Cell[CellGroupData[{
Cell[91042, 2086, 142, 3, 154, "Input"],
Cell[91187, 2091, 138, 3, 154, "Output"]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[91374, 2100, 52, 1, 90, "Subsubsection"],
Cell[91429, 2103, 73, 1, 656, "Input"],
Cell[91505, 2106, 142, 6, 512, "Text"],
Cell[91650, 2114, 193, 6, 640, "Input"],
Cell[91846, 2122, 45, 1, 512, "Text"],
Cell[CellGroupData[{
Cell[91916, 2127, 209, 7, 640, "Input"],
Cell[92128, 2136, 307, 9, 640, "Output"]
}, Open  ]],
Cell[92450, 2148, 105, 2, 512, "Text"],
Cell[92558, 2152, 193, 6, 640, "Input"],
Cell[92754, 2160, 45, 1, 512, "Text"],
Cell[CellGroupData[{
Cell[92824, 2165, 236, 7, 640, "Input"],
Cell[93063, 2174, 307, 9, 640, "Output"]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[93419, 2189, 48, 1, 90, "Subsubsection"],
Cell[93470, 2192, 267, 8, 256, "Text"],
Cell[93740, 2202, 204, 6, 308, "Input"],
Cell[93947, 2210, 45, 1, 256, "Text"],
Cell[CellGroupData[{
Cell[94017, 2215, 269, 5, 308, "Input"],
Cell[94289, 2222, 422, 14, 308, "Output"]
}, Open  ]],
Cell[94726, 2239, 576, 17, 436, "Text"],
Cell[95305, 2258, 350, 12, 336, "Input"],
Cell[CellGroupData[{
Cell[95680, 2274, 303, 8, 304, "Input"],
Cell[95986, 2284, 340, 11, 332, "Output"]
}, Open  ]],
Cell[96341, 2298, 116, 1, 220, "Text"],
Cell[96460, 2301, 159, 5, 312, "Input"],
Cell[96622, 2308, 211, 7, 312, "Input"],
Cell[CellGroupData[{
Cell[96858, 2319, 210, 7, 304, "Input"],
Cell[97071, 2328, 171, 5, 316, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[97279, 2338, 212, 7, 304, "Input"],
Cell[97494, 2347, 198, 6, 316, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[97729, 2358, 210, 7, 304, "Input"],
Cell[97942, 2367, 627, 22, 332, "Output"]
}, Open  ]],
Cell[98584, 2392, 169, 6, 256, "Text"],
Cell[98756, 2400, 305, 9, 320, "Input"],
Cell[99064, 2411, 42, 1, 256, "Text"],
Cell[CellGroupData[{
Cell[99131, 2416, 188, 5, 304, "Input"],
Cell[99322, 2423, 336, 10, 316, "Output"]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[99707, 2439, 56, 1, 90, "Subsubsection"],
Cell[99766, 2442, 73, 1, 308, "Input"],
Cell[99842, 2445, 117, 2, 256, "Text"],
Cell[99962, 2449, 191, 6, 452, "Input"],
Cell[100156, 2457, 45, 1, 256, "Text"],
Cell[100204, 2460, 1319, 40, 372, "Text"],
Cell[101526, 2502, 88, 1, 220, "Text"],
Cell[101617, 2505, 294, 10, 464, "Input"],
Cell[101914, 2517, 114, 1, 220, "Text"],
Cell[CellGroupData[{
Cell[102053, 2522, 174, 4, 308, "Input"],
Cell[102230, 2528, 439, 15, 472, "Output"]
}, Open  ]],
Cell[102684, 2546, 124, 1, 220, "Text"],
Cell[102811, 2549, 159, 5, 312, "Input"],
Cell[102973, 2556, 211, 7, 312, "Input"],
Cell[CellGroupData[{
Cell[103209, 2567, 144, 4, 304, "Input"],
Cell[103356, 2573, 242, 7, 344, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[103635, 2585, 144, 4, 304, "Input"],
Cell[103782, 2591, 267, 8, 344, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[104086, 2604, 595, 16, 456, "Input"],
Cell[104684, 2622, 536, 17, 472, "Output"]
}, Open  ]],
Cell[105235, 2642, 98, 1, 220, "Text"],
Cell[CellGroupData[{
Cell[105358, 2647, 256, 7, 304, "Input"],
Cell[105617, 2656, 469, 16, 472, "Output"]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[106135, 2678, 66, 1, 90, "Subsubsection"],
Cell[106204, 2681, 73, 1, 616, "Input"],
Cell[106280, 2684, 164, 5, 616, "Input"],
Cell[106447, 2691, 385, 13, 616, "Input"],
Cell[106835, 2706, 196, 7, 672, "Text"],
Cell[107034, 2715, 182, 6, 744, "Input"],
Cell[CellGroupData[{
Cell[107241, 2725, 144, 4, 616, "Input"],
Cell[107388, 2731, 274, 10, 1024, "Output"]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[107711, 2747, 64, 1, 90, "Subsubsection"],
Cell[107778, 2750, 388, 14, 768, "Text"],
Cell[108169, 2766, 60, 1, 512, "Text"],
Cell[108232, 2769, 71, 1, 856, "Text"],
Cell[108306, 2772, 354, 14, 752, "Text"],
Cell[108663, 2788, 706, 26, 1328, "Text"]
}, Closed]],
Cell[CellGroupData[{
Cell[109406, 2819, 171, 4, 90, "Subsubsection"],
Cell[109580, 2825, 53, 1, 1024, "Text"],
Cell[109636, 2828, 408, 15, 1536, "Text"],
Cell[110047, 2845, 199, 5, 1696, "Text"],
Cell[110249, 2852, 456, 14, 1024, "Text"],
Cell[110708, 2868, 57, 1, 1024, "Text"],
Cell[110768, 2871, 399, 14, 1504, "Text"],
Cell[111170, 2887, 72, 1, 1024, "Text"],
Cell[111245, 2890, 756, 26, 1536, "Text"]
}, Closed]],
Cell[CellGroupData[{
Cell[112038, 2921, 76, 1, 90, "Subsubsection"],
Cell[112117, 2924, 73, 1, 616, "Input"],
Cell[112193, 2927, 173, 5, 616, "Input"],
Cell[112369, 2934, 423, 14, 616, "Input"],
Cell[112795, 2950, 38, 1, 512, "Text"],
Cell[112836, 2953, 169, 5, 616, "Input"],
Cell[113008, 2960, 134, 4, 616, "Input"],
Cell[113145, 2966, 225, 7, 616, "Input"],
Cell[113373, 2975, 245, 8, 616, "Input"],
Cell[CellGroupData[{
Cell[113643, 2987, 292, 9, 616, "Input"],
Cell[113938, 2998, 253, 9, 768, "Output"]
}, Open  ]]
}, Closed]]
}, Closed]],
Cell[CellGroupData[{
Cell[114252, 3014, 108, 1, 87, "Section"],
Cell[CellGroupData[{
Cell[114385, 3019, 1835, 61, 282, "Subsection"],
Cell[116223, 3082, 359, 9, 156, "Input"],
Cell[CellGroupData[{
Cell[116607, 3095, 140, 3, 154, "Input"],
Cell[116750, 3100, 300, 8, 154, "Output"]
}, Open  ]],
Cell[117065, 3111, 383, 11, 220, "Input"],
Cell[117451, 3124, 369, 6, 110, "Text"],
Cell[117823, 3132, 407, 11, 156, "Input"],
Cell[118233, 3145, 623, 23, 140, "Text"],
Cell[CellGroupData[{
Cell[118881, 3172, 186, 4, 154, "Input"],
Cell[119070, 3178, 325, 10, 228, "Output"]
}, Open  ]],
Cell[119410, 3191, 121, 2, 110, "Text"],
Cell[119534, 3195, 321, 9, 156, "Input"],
Cell[119858, 3206, 710, 20, 180, "Text"],
Cell[CellGroupData[{
Cell[120593, 3230, 137, 3, 154, "Input"],
Cell[120733, 3235, 373, 10, 158, "Output"]
}, Open  ]],
Cell[121121, 3248, 390, 10, 226, "Input"],
Cell[121514, 3260, 1188, 33, 186, "Text"],
Cell[CellGroupData[{
Cell[122727, 3297, 142, 3, 154, "Input"],
Cell[122872, 3302, 412, 14, 226, "Output"]
}, Open  ]],
Cell[123299, 3319, 359, 9, 218, "Input"],
Cell[123661, 3330, 1011, 35, 454, "Text"],
Cell[CellGroupData[{
Cell[124697, 3369, 172, 4, 154, "Input"],
Cell[124872, 3375, 215, 6, 206, "Output"]
}, Open  ]],
Cell[125102, 3384, 352, 8, 156, "Input"],
Cell[CellGroupData[{
Cell[125479, 3396, 166, 4, 154, "Input"],
Cell[125648, 3402, 286, 8, 160, "Output"]
}, Open  ]],
Cell[125949, 3413, 445, 11, 166, "Input"],
Cell[CellGroupData[{
Cell[126419, 3428, 166, 4, 154, "Input"],
Cell[126588, 3434, 501, 16, 232, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[127126, 3455, 159, 2, 106, "Subsubsection"],
Cell[127288, 3459, 40249, 665, 1528, "Text"],
Cell[167540, 4126, 156, 2, 110, "Text"]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[167745, 4134, 2006, 55, 230, "Subsection"],
Cell[169754, 4191, 28653, 475, 804, "Text"],
Cell[198410, 4668, 178, 2, 110, "Text"],
Cell[198591, 4672, 1792, 50, 256, "Input"],
Cell[CellGroupData[{
Cell[200408, 4726, 140, 3, 154, "Input"],
Cell[200551, 4731, 1852, 54, 314, "Output"]
}, Open  ]]
}, Closed]]
}, Closed]],
Cell[CellGroupData[{
Cell[202464, 4792, 163, 2, 87, "Section"],
Cell[202630, 4796, 1670, 42, 306, "Text"],
Cell[204303, 4840, 1070, 32, 358, "Text"],
Cell[CellGroupData[{
Cell[205398, 4876, 315, 8, 200, "Subsubsection"],
Cell[205716, 4886, 52, 1, 128, "Text"],
Cell[205771, 4889, 1172, 37, 340, "Text"],
Cell[206946, 4928, 57, 1, 128, "Text"],
Cell[207006, 4931, 1251, 37, 322, "Text"],
Cell[208260, 4970, 213, 5, 212, "Text"],
Cell[208476, 4977, 64, 1, 128, "Text"],
Cell[208543, 4980, 69, 1, 128, "Text"]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[208661, 4987, 336, 6, 87, "Section"],
Cell[CellGroupData[{
Cell[209022, 4997, 150, 3, 146, "Subsection"],
Cell[209175, 5002, 327, 10, 112, "Text"],
Cell[209505, 5014, 190, 6, 156, "Input"],
Cell[209698, 5022, 186, 6, 110, "Text"],
Cell[209887, 5030, 256, 8, 156, "Input"],
Cell[210146, 5040, 154, 3, 110, "Text"],
Cell[CellGroupData[{
Cell[210325, 5047, 345, 11, 152, "Input"],
Cell[210673, 5060, 1172, 27, 788, "Output"]
}, Open  ]],
Cell[211860, 5090, 124, 3, 110, "Text"],
Cell[211987, 5095, 193, 6, 152, "Input"],
Cell[212183, 5103, 679, 23, 176, "Text"],
Cell[CellGroupData[{
Cell[212887, 5130, 144, 4, 152, "Input"],
Cell[213034, 5136, 566, 17, 166, "Output"]
}, Open  ]],
Cell[213615, 5156, 78, 2, 110, "Text"],
Cell[213696, 5160, 1205, 42, 156, "Text"],
Cell[CellGroupData[{
Cell[214926, 5206, 197, 6, 456, "Input"],
Cell[215126, 5214, 891, 27, 476, "Output"]
}, Open  ]],
Cell[216032, 5244, 112, 3, 352, "Text"],
Cell[216147, 5249, 162, 5, 304, "Input"],
Cell[216312, 5256, 204, 7, 220, "Text"],
Cell[216519, 5265, 193, 6, 304, "Input"],
Cell[CellGroupData[{
Cell[216737, 5275, 83, 2, 304, "Input"],
Cell[216823, 5279, 336, 10, 316, "Output"]
}, Open  ]],
Cell[217174, 5292, 40, 0, 220, "Text"],
Cell[CellGroupData[{
Cell[217239, 5296, 144, 4, 304, "Input"],
Cell[217386, 5302, 485, 15, 316, "Output"]
}, Open  ]],
Cell[217886, 5320, 194, 6, 220, "Text"],
Cell[218083, 5328, 69, 0, 220, "Text"],
Cell[218155, 5330, 193, 6, 304, "Input"],
Cell[CellGroupData[{
Cell[218373, 5340, 83, 2, 304, "Input"],
Cell[218459, 5344, 607, 19, 332, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[219103, 5368, 119, 3, 304, "Input"],
Cell[219225, 5373, 419, 13, 332, "Output"]
}, Open  ]],
Cell[219659, 5389, 94, 2, 220, "Text"],
Cell[CellGroupData[{
Cell[219778, 5395, 410, 12, 308, "Input"],
Cell[220191, 5409, 2137, 40, 1896, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[222365, 5454, 237, 7, 456, "Input"],
Cell[222605, 5463, 513, 15, 436, "Output"]
}, Open  ]],
Cell[223133, 5481, 106, 3, 352, "Text"],
Cell[CellGroupData[{
Cell[223264, 5488, 399, 12, 308, "Input"],
Cell[223666, 5502, 2801, 51, 1820, "Output"]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[226516, 5559, 224, 4, 106, "Subsection"],
Cell[226743, 5565, 346, 10, 112, "Text"],
Cell[227092, 5577, 224, 7, 214, "Input"],
Cell[227319, 5586, 224, 5, 112, "Text"],
Cell[227546, 5593, 152, 4, 154, "Input"],
Cell[227701, 5599, 142, 3, 110, "Text"],
Cell[227846, 5604, 142, 5, 164, "Text"],
Cell[CellGroupData[{
Cell[228013, 5613, 357, 12, 228, "Input"],
Cell[228373, 5627, 219, 6, 208, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[228629, 5638, 150, 4, 154, "Input"],
Cell[228782, 5644, 9296, 159, 958, "Output"]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[238127, 5809, 175, 3, 106, "Subsection"],
Cell[238305, 5814, 374, 10, 112, "Text"],
Cell[238682, 5826, 149, 6, 110, "Text"],
Cell[238834, 5834, 216, 7, 110, "Text"],
Cell[239053, 5843, 238, 9, 110, "Text"],
Cell[239294, 5854, 454, 17, 112, "Text"],
Cell[239751, 5873, 74, 2, 110, "Text"],
Cell[239828, 5877, 246, 9, 110, "Text"],
Cell[240077, 5888, 137, 3, 110, "Text"],
Cell[240217, 5893, 159, 6, 110, "Text"],
Cell[240379, 5901, 292, 12, 110, "Text"],
Cell[240674, 5915, 234, 8, 110, "Text"],
Cell[240911, 5925, 410, 17, 110, "Text"],
Cell[241324, 5944, 366, 14, 110, "Text"],
Cell[241693, 5960, 64, 0, 110, "Text"],
Cell[241760, 5962, 209, 8, 110, "Text"],
Cell[241972, 5972, 245, 10, 118, "Text"],
Cell[242220, 5984, 130, 5, 220, "Text"],
Cell[242353, 5991, 73, 2, 220, "Text"],
Cell[242429, 5995, 170, 5, 220, "Text"],
Cell[242602, 6002, 24, 0, 220, "Text"],
Cell[242629, 6004, 414, 15, 328, "Text"],
Cell[243046, 6021, 192, 8, 220, "Text"],
Cell[243241, 6031, 159, 5, 308, "Text"],
Cell[243403, 6038, 263, 10, 224, "Text"],
Cell[243669, 6050, 388, 6, 616, "Text"],
Cell[CellGroupData[{
Cell[244082, 6060, 212, 7, 212, "Subsubsection"],
Cell[244297, 6069, 728, 27, 348, "Text"],
Cell[245028, 6098, 30, 0, 220, "Text"],
Cell[245061, 6100, 477, 19, 276, "Text"],
Cell[245541, 6121, 731, 28, 356, "Text"]
}, Open  ]],
Cell[246287, 6152, 50, 0, 212, "Subsubsection"],
Cell[CellGroupData[{
Cell[246362, 6156, 274, 11, 148, "Subsubsection"],
Cell[246639, 6169, 206, 8, 1124352, "Text"],
Cell[246848, 6179, 158, 6, 1124352, "Text"],
Cell[247009, 6187, 302, 12, 1290240, "Text"]
}, Closed]],
Cell[CellGroupData[{
Cell[247348, 6204, 424, 16, 272, "Subsubsection"],
Cell[247775, 6222, 104, 4, 64512, "Text"],
Cell[247882, 6228, 563, 24, 85248, "Text"],
Cell[248448, 6254, 157, 3, 63360, "Text"]
}, Closed]]
}, Closed]],
Cell[CellGroupData[{
Cell[248654, 6263, 43, 0, 106, "Subsection"],
Cell[248700, 6265, 370, 14, 130, "Text"],
Cell[249073, 6281, 375, 16, 158, "Text"],
Cell[249451, 6299, 502, 16, 136, "Text"],
Cell[249956, 6317, 153, 6, 128, "Text"],
Cell[CellGroupData[{
Cell[250134, 6327, 45, 1, 122, "Subsubsection"],
Cell[250182, 6330, 256, 10, 320, "Input"],
Cell[250441, 6342, 399, 15, 432, "Text"],
Cell[CellGroupData[{
Cell[250865, 6361, 274, 10, 432, "Input"],
Cell[251142, 6373, 136, 4, 344, "Output"]
}, Open  ]],
Cell[251293, 6380, 217, 5, 760, "Text"],
Cell[251513, 6387, 143, 4, 592, "Text"],
Cell[CellGroupData[{
Cell[251681, 6395, 181, 5, 308, "Input"],
Cell[251865, 6402, 2805, 53, 1944, "Output"]
}, Open  ]]
}, Closed]]
}, Closed]],
Cell[CellGroupData[{
Cell[254731, 6462, 92, 2, 106, "Subsection"],
Cell[254826, 6466, 111, 3, 128, "Text"],
Cell[254940, 6471, 270, 8, 128, "Text"],
Cell[255213, 6481, 99, 3, 128, "Text"],
Cell[255315, 6486, 169, 4, 128, "Text"],
Cell[255487, 6492, 639, 25, 188, "Text"],
Cell[256129, 6519, 43, 1, 128, "Text"],
Cell[256175, 6522, 613, 24, 188, "Text"],
Cell[256791, 6548, 801, 31, 174, "Text"],
Cell[257595, 6581, 150, 4, 128, "Text"]
}, Closed]]
}, Closed]],
Cell[CellGroupData[{
Cell[257794, 6591, 38, 0, 87, "Section"],
Cell[CellGroupData[{
Cell[257857, 6595, 41, 0, 106, "Subsubsection"],
Cell[257901, 6597, 363, 15, 110, "Text"],
Cell[258267, 6614, 459, 17, 168, "Text"]
}, Open  ]],
Cell[CellGroupData[{
Cell[258763, 6636, 34, 0, 106, "Subsubsection"],
Cell[258800, 6638, 570, 21, 182, "Text"],
Cell[259373, 6661, 636, 24, 186, "Text"]
}, Open  ]],
Cell[CellGroupData[{
Cell[260046, 6690, 41, 0, 106, "Subsubsection"],
Cell[260090, 6692, 223, 6, 110, "Text"],
Cell[260316, 6700, 351, 12, 168, "Text"],
Cell[260670, 6714, 200, 7, 110, "Text"],
Cell[260873, 6723, 554, 19, 168, "Text"],
Cell[261430, 6744, 606, 22, 168, "Text"],
Cell[262039, 6768, 83, 2, 110, "Text"]
}, Open  ]],
Cell[CellGroupData[{
Cell[262159, 6775, 33, 0, 106, "Subsubsection"],
Cell[262195, 6777, 352, 11, 162, "Text"],
Cell[262550, 6790, 134, 3, 110, "Text"],
Cell[262687, 6795, 873, 32, 200, "Text"],
Cell[263563, 6829, 1580, 54, 174, "Text"]
}, Open  ]]
}, Closed]]
}, Open  ]]
}
]
*)

(* End of internal cache information *)

(* NotebookSignature gvpS@ihZlTQkICwuKWYgAVUF *)