(* Content-type: application/mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 6.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       145,          7]
NotebookDataLength[     27822,        931]
NotebookOptionsPosition[     25376,        838]
NotebookOutlinePosition[     25904,        859]
CellTagsIndexPosition[     25861,        856]
WindowFrame->Normal
ContainsDynamic->False*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell["\<\
Exercices de d\[EAcute]rivation de fonctions compos\[EAcute]es\
\>", "Section",
 CellChangeTimes->{{3.398430879634953*^9, 3.398430882832155*^9}},
 FontColor->RGBColor[0, 0.500999, 0.500999]],

Cell[CellGroupData[{

Cell["\<\
D\[EAcute]river les fonctions suivantes\
\>", "Subsection",
 FontColor->RGBColor[0.501961, 0, 0]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"Clear", "[", "f", "]"}], ";", 
  RowBox[{"i", "=", "1"}], ";"}], "\n", 
 RowBox[{
  RowBox[{"a", "=", 
   RowBox[{"RandomInteger", "[", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "5"}], ",", "5"}], "}"}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"b", "=", 
   RowBox[{"RandomInteger", "[", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "5"}], ",", "5"}], "}"}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"c", "=", 
   RowBox[{"RandomInteger", "[", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "5"}], ",", "5"}], "}"}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{
   RowBox[{"f", "[", "x", "]"}], ":=", 
   RowBox[{"Sqrt", "[", 
    RowBox[{
     RowBox[{"5", 
      RowBox[{"x", "^", "2"}]}], "-", 
     RowBox[{"3", "x"}], "+", "2"}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{
   RowBox[{"sol", "[", "1", "]"}], "=", 
   RowBox[{"Simplify", "[", 
    RowBox[{
     SubscriptBox["\[PartialD]", "x"], 
     RowBox[{"f", "[", "x", "]"}]}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"Print", "[", 
   RowBox[{"i", ",", "\"\<)  f(x) = \>\"", ",", 
    RowBox[{"f", "[", "x", "]"}]}], "]"}], ";"}]}], "Input",
 CellOpen->False,
 CellChangeTimes->{{3.398430634088985*^9, 3.398430640493*^9}},
 FontSize->13,
 FontColor->RGBColor[0, 0.500999, 0.500999]],

Cell[BoxData[
 FormBox[
  InterpretationBox[
   RowBox[{
   "1", "\[InvisibleSpace]", "\<\")  f(x) = \"\>", "\[InvisibleSpace]", 
    SqrtBox[
     RowBox[{
      RowBox[{"5", " ", 
       SuperscriptBox["x", "2"]}], "-", 
      RowBox[{"3", " ", "x"}], "+", "2"}]]}],
   SequenceForm[
   1, ")  f(x) = ", (2 - 3 $CellContext`x + 5 $CellContext`x^2)^
    Rational[1, 2]],
   Editable->False], TraditionalForm]], "Print",
 CellChangeTimes->{
  3.398430642984667*^9, 3.3984308736179543`*^9, 3.398430977910754*^9, {
   3.3984312352890387`*^9, 3.3984312574266653`*^9}},
 FontColor->RGBColor[0, 0.500999, 0.500999]]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"Clear", "[", "f", "]"}], ";", 
  RowBox[{"i", "=", 
   RowBox[{"i", "+", "1"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"a", "=", 
   RowBox[{"RandomInteger", "[", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "5"}], ",", "5"}], "}"}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"b", "=", 
   RowBox[{"RandomInteger", "[", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "5"}], ",", "5"}], "}"}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"c", "=", 
   RowBox[{"RandomInteger", "[", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "5"}], ",", "5"}], "}"}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{
   RowBox[{"f", "[", "x", "]"}], ":=", 
   RowBox[{
    RowBox[{"(", 
     RowBox[{"8", "-", 
      RowBox[{"5", 
       RowBox[{"x", "^", "2"}]}]}], ")"}], "^", "2"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{
   RowBox[{"sol", "[", "i", "]"}], "=", 
   RowBox[{"Simplify", "[", 
    RowBox[{
     SubscriptBox["\[PartialD]", "x"], 
     RowBox[{"f", "[", "x", "]"}]}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"Print", "[", 
   RowBox[{"i", ",", "\"\<)  f(x) = \>\"", ",", 
    RowBox[{"f", "[", "x", "]"}]}], "]"}], ";"}]}], "Input",
 CellOpen->False,
 CellChangeTimes->{{3.398430649734797*^9, 3.398430657459084*^9}},
 FontSize->13,
 FontColor->RGBColor[0, 0.500999, 0.500999]],

Cell[BoxData[
 FormBox[
  InterpretationBox[
   RowBox[{
   "2", "\[InvisibleSpace]", "\<\")  f(x) = \"\>", "\[InvisibleSpace]", 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{"8", "-", 
       RowBox[{"5", " ", 
        SuperscriptBox["x", "2"]}]}], ")"}], "2"]}],
   SequenceForm[2, ")  f(x) = ", (8 - 5 $CellContext`x^2)^2],
   Editable->False], TraditionalForm]], "Print",
 CellChangeTimes->{
  3.398430659561411*^9, 3.398430873713797*^9, 3.398430977995384*^9, {
   3.39843123537346*^9, 3.398431257512909*^9}},
 FontColor->RGBColor[0, 0.500999, 0.500999]]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"Clear", "[", "f", "]"}], ";", 
  RowBox[{"i", "=", "3"}], ";"}], "\n", 
 RowBox[{
  RowBox[{
   RowBox[{"f", "[", "x", "]"}], ":=", 
   RowBox[{"1", "/", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{
       RowBox[{"3", "x"}], "-", "1"}], ")"}], "^", "3"}]}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{
   RowBox[{"sol", "[", "i", "]"}], ":=", 
   RowBox[{"Simplify", "[", 
    RowBox[{
     SubscriptBox["\[PartialD]", "x"], 
     RowBox[{"f", "[", "x", "]"}]}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"Print", "[", 
   RowBox[{"i", ",", "\"\<)  f(x) = \>\"", ",", 
    RowBox[{"f", "[", "x", "]"}]}], "]"}], ";"}]}], "Input",
 CellOpen->False,
 CellChangeTimes->{{3.398430666080855*^9, 3.398430674603825*^9}, 
   3.3984310391267567`*^9},
 FontSize->13,
 FontColor->RGBColor[0, 0.500999, 0.500999]],

Cell[BoxData[
 FormBox[
  InterpretationBox[
   RowBox[{
   "3", "\[InvisibleSpace]", "\<\")  f(x) = \"\>", "\[InvisibleSpace]", 
    FractionBox["1", 
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{
        RowBox[{"3", " ", "x"}], "-", "1"}], ")"}], "3"]]}],
   SequenceForm[3, ")  f(x) = ", (-1 + 3 $CellContext`x)^(-3)],
   Editable->False], TraditionalForm]], "Print",
 CellChangeTimes->{
  3.398430677488142*^9, 3.3984308737460423`*^9, 3.3984309780362*^9, 
   3.398431039466642*^9, {3.3984312354145203`*^9, 3.398431257542362*^9}},
 FontColor->RGBColor[0, 0.500999, 0.500999]]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"Clear", "[", "f", "]"}], ";", 
  RowBox[{"i", "=", "4"}], ";"}], "\n", 
 RowBox[{
  RowBox[{
   RowBox[{"f", "[", "x", "]"}], ":=", 
   RowBox[{"Sin", "[", 
    RowBox[{"1", "-", 
     RowBox[{"2", 
      RowBox[{"x", "^", "2"}]}]}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{
   RowBox[{"sol", "[", "i", "]"}], "=", 
   RowBox[{"Simplify", "[", 
    RowBox[{
     SubscriptBox["\[PartialD]", "x"], 
     RowBox[{"f", "[", "x", "]"}]}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"Print", "[", 
   RowBox[{"i", ",", "\"\<)  f(x) = \>\"", ",", 
    RowBox[{"f", "[", "x", "]"}]}], "]"}], ";"}]}], "Input",
 CellOpen->False,
 CellChangeTimes->{{3.398430682151387*^9, 3.398430690717164*^9}, {
  3.398431086095563*^9, 3.398431117955659*^9}},
 FontSize->13,
 FontColor->RGBColor[0, 0.500999, 0.500999]],

Cell[BoxData[
 FormBox[
  InterpretationBox[
   RowBox[{
   "4", "\[InvisibleSpace]", "\<\")  f(x) = \"\>", "\[InvisibleSpace]", 
    RowBox[{"sin", "(", 
     RowBox[{"1", "-", 
      RowBox[{"2", " ", 
       SuperscriptBox["x", "2"]}]}], ")"}]}],
   SequenceForm[4, ")  f(x) = ", 
    Sin[1 - 2 $CellContext`x^2]],
   Editable->False], TraditionalForm]], "Print",
 CellChangeTimes->{{3.398430693045059*^9, 3.3984307089316*^9}, 
   3.398430873780491*^9, 3.398430978062772*^9, 3.3984311201119432`*^9, {
   3.398431235444915*^9, 3.398431257578588*^9}},
 FontColor->RGBColor[0, 0.500999, 0.500999]]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"Clear", "[", "f", "]"}], ";", 
  RowBox[{"i", "=", "5"}], ";"}], "\n", 
 RowBox[{
  RowBox[{
   RowBox[{"f", "[", "x", "]"}], ":=", 
   RowBox[{
    RowBox[{"Sin", "[", "x", "]"}], "^", "3"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{
   RowBox[{"sol", "[", "i", "]"}], "=", 
   RowBox[{"Simplify", "[", 
    RowBox[{
     SubscriptBox["\[PartialD]", "x"], 
     RowBox[{"f", "[", "x", "]"}]}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"Print", "[", 
   RowBox[{"i", ",", "\"\<)  f(x) = \>\"", ",", 
    RowBox[{"f", "[", "x", "]"}]}], "]"}], ";"}]}], "Input",
 CellOpen->False,
 CellChangeTimes->{{3.398430717815235*^9, 3.3984307710880337`*^9}, {
  3.39843113543885*^9, 3.39843117733987*^9}},
 FontSize->13,
 FontColor->RGBColor[0, 0.500999, 0.500999]],

Cell[BoxData[
 FormBox[
  InterpretationBox[
   RowBox[{
   "5", "\[InvisibleSpace]", "\<\")  f(x) = \"\>", "\[InvisibleSpace]", 
    RowBox[{
     SuperscriptBox["sin", "3"], "(", "x", ")"}]}],
   SequenceForm[5, ")  f(x) = ", Sin[$CellContext`x]^3],
   Editable->False], TraditionalForm]], "Print",
 CellChangeTimes->{{3.398430723124758*^9, 3.398430771599242*^9}, 
   3.398430873848722*^9, 3.398430978102867*^9, {3.398431150401104*^9, 
   3.398431178020874*^9}, {3.3984312354812307`*^9, 3.3984312576185637`*^9}},
 FontColor->RGBColor[0, 0.500999, 0.500999]]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"Clear", "[", "f", "]"}], ";", 
  RowBox[{"i", "=", 
   RowBox[{"i", "+", "1"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"a", "=", 
   RowBox[{"RandomInteger", "[", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "5"}], ",", "5"}], "}"}], "]"}]}], ";", 
  RowBox[{"b", "=", 
   RowBox[{"RandomInteger", "[", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "5"}], ",", "5"}], "}"}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"c", "=", 
   RowBox[{"RandomInteger", "[", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "5"}], ",", "5"}], "}"}], "]"}]}], ";", 
  RowBox[{"d", "=", 
   RowBox[{"RandomInteger", "[", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "5"}], ",", "5"}], "}"}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{
   RowBox[{"f", "[", "x", "]"}], ":=", 
   RowBox[{"Cos", "[", 
    RowBox[{"Sqrt", "[", "x", "]"}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{
   RowBox[{"sol", "[", "i", "]"}], "=", 
   RowBox[{"Simplify", "[", 
    RowBox[{
     SubscriptBox["\[PartialD]", "x"], 
     RowBox[{"f", "[", "x", "]"}]}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"Print", "[", 
   RowBox[{"i", ",", "\"\<)  f(x) = \>\"", ",", 
    RowBox[{"f", "[", "x", "]"}]}], "]"}], ";"}]}], "Input",
 CellOpen->False,
 CellChangeTimes->{{3.398430793679229*^9, 3.398430804555122*^9}},
 FontColor->RGBColor[0, 0.500999, 0.500999]],

Cell[BoxData[
 FormBox[
  InterpretationBox[
   RowBox[{
   "6", "\[InvisibleSpace]", "\<\")  f(x) = \"\>", "\[InvisibleSpace]", 
    RowBox[{"cos", "(", 
     SqrtBox["x"], ")"}]}],
   SequenceForm[6, ")  f(x) = ", 
    Cos[$CellContext`x^Rational[1, 2]]],
   Editable->False], TraditionalForm]], "Print",
 CellChangeTimes->{
  3.398430805633465*^9, 3.398430873913068*^9, 3.3984309781426353`*^9, {
   3.398431235520282*^9, 3.3984312576590757`*^9}},
 FontColor->RGBColor[0, 0.500999, 0.500999]]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"Clear", "[", "f", "]"}], ";", 
  RowBox[{"i", "=", 
   RowBox[{"i", "+", "1"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"a", "=", 
   RowBox[{"RandomInteger", "[", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "5"}], ",", "5"}], "}"}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"b", "=", 
   RowBox[{"RandomInteger", "[", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "5"}], ",", "5"}], "}"}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"c", "=", 
   RowBox[{"RandomInteger", "[", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "5"}], ",", "5"}], "}"}], "]"}]}], ";", 
  RowBox[{"d", "=", 
   RowBox[{"RandomInteger", "[", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "5"}], ",", "5"}], "}"}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{
   RowBox[{"f", "[", "x", "]"}], ":=", 
   RowBox[{"Sin", "[", 
    RowBox[{"1", "/", "x"}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{
   RowBox[{"sol", "[", "i", "]"}], "=", 
   RowBox[{"Simplify", "[", 
    RowBox[{
     SubscriptBox["\[PartialD]", "x"], 
     RowBox[{"f", "[", "x", "]"}]}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"Print", "[", 
   RowBox[{"i", ",", "\"\<)  f(x) = \>\"", ",", 
    RowBox[{"f", "[", "x", "]"}]}], "]"}], ";"}]}], "Input",
 CellOpen->False,
 CellChangeTimes->{{3.398430810311578*^9, 3.3984308171893873`*^9}},
 FontColor->RGBColor[0, 0.500999, 0.500999]],

Cell[BoxData[
 FormBox[
  InterpretationBox[
   RowBox[{
   "7", "\[InvisibleSpace]", "\<\")  f(x) = \"\>", "\[InvisibleSpace]", 
    RowBox[{"sin", "(", 
     FractionBox["1", "x"], ")"}]}],
   SequenceForm[7, ")  f(x) = ", 
    Sin[$CellContext`x^(-1)]],
   Editable->False], TraditionalForm]], "Print",
 CellChangeTimes->{
  3.398430817993181*^9, 3.3984308739543657`*^9, 3.3984309781825047`*^9, {
   3.398431235561225*^9, 3.398431257699045*^9}},
 FontColor->RGBColor[0, 0.500999, 0.500999]]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"Clear", "[", "f", "]"}], ";", 
  RowBox[{"i", "=", "8"}], ";"}], "\n", 
 RowBox[{
  RowBox[{
   RowBox[{"f", "[", "x", "]"}], ":=", 
   RowBox[{
    RowBox[{"Sin", "[", "x", "]"}], " ", 
    RowBox[{"Cos", "[", 
     RowBox[{"3", "x"}], "]"}]}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{
   RowBox[{"sol", "[", "i", "]"}], "=", 
   RowBox[{"Simplify", "[", 
    RowBox[{
     SubscriptBox["\[PartialD]", "x"], 
     RowBox[{"f", "[", "x", "]"}]}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"Print", "[", 
   RowBox[{"i", ",", "\"\<)  f(x) = \>\"", ",", 
    RowBox[{"f", "[", "x", "]"}]}], "]"}], ";"}]}], "Input",
 CellOpen->False,
 CellChangeTimes->{{3.398430826543549*^9, 3.398430829276363*^9}, {
  3.39843120490593*^9, 3.398431247787314*^9}},
 FontColor->RGBColor[0, 0.500999, 0.500999]],

Cell[BoxData[
 FormBox[
  InterpretationBox[
   RowBox[{
   "8", "\[InvisibleSpace]", "\<\")  f(x) = \"\>", "\[InvisibleSpace]", 
    RowBox[{
     RowBox[{"cos", "(", 
      RowBox[{"3", " ", "x"}], ")"}], " ", 
     RowBox[{"sin", "(", "x", ")"}]}]}],
   SequenceForm[8, ")  f(x) = ", Cos[3 $CellContext`x] Sin[$CellContext`x]],
   Editable->False], TraditionalForm]], "Print",
 CellChangeTimes->{
  3.398430830175439*^9, 3.3984308739931393`*^9, 3.398430978224401*^9, {
   3.3984312228098803`*^9, 3.398431257738758*^9}},
 FontColor->RGBColor[0, 0.500999, 0.500999]]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"Clear", "[", "f", "]"}], ";", 
  RowBox[{"i", "=", 
   RowBox[{"i", "+", "1"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"a", "=", 
   RowBox[{"RandomInteger", "[", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "5"}], ",", "5"}], "}"}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"b", "=", 
   RowBox[{"RandomInteger", "[", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "5"}], ",", "5"}], "}"}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"c", "=", 
   RowBox[{"RandomInteger", "[", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "5"}], ",", "5"}], "}"}], "]"}]}], ";", 
  RowBox[{"d", "=", 
   RowBox[{"RandomInteger", "[", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "5"}], ",", "5"}], "}"}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{
   RowBox[{"f", "[", "x", "]"}], ":=", 
   RowBox[{"Sin", "[", 
    RowBox[{"x", "/", 
     RowBox[{"(", 
      RowBox[{"x", "-", "2"}], ")"}]}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{
   RowBox[{"sol", "[", "i", "]"}], "=", 
   RowBox[{"Simplify", "[", 
    RowBox[{
     SubscriptBox["\[PartialD]", "x"], 
     RowBox[{"f", "[", "x", "]"}]}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"Print", "[", 
   RowBox[{"i", ",", "\"\<)  f(x) = \>\"", ",", 
    RowBox[{"f", "[", "x", "]"}]}], "]"}], ";"}]}], "Input",
 CellOpen->False,
 CellChangeTimes->{{3.398430834815709*^9, 3.398430841253227*^9}},
 FontColor->RGBColor[0, 0.500999, 0.500999]],

Cell[BoxData[
 FormBox[
  InterpretationBox[
   RowBox[{
   "9", "\[InvisibleSpace]", "\<\")  f(x) = \"\>", "\[InvisibleSpace]", 
    RowBox[{"sin", "(", 
     FractionBox["x", 
      RowBox[{"x", "-", "2"}]], ")"}]}],
   SequenceForm[9, ")  f(x) = ", 
    Sin[(-2 + $CellContext`x)^(-1) $CellContext`x]],
   Editable->False], TraditionalForm]], "Print",
 CellChangeTimes->{
  3.39843084197313*^9, 3.398430874034693*^9, 3.398430978263054*^9, {
   3.398431235640971*^9, 3.39843125777876*^9}},
 FontColor->RGBColor[0, 0.500999, 0.500999]]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"Clear", "[", "f", "]"}], ";", 
  RowBox[{"i", "=", 
   RowBox[{"i", "+", "1"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"a", "=", 
   RowBox[{"RandomInteger", "[", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "5"}], ",", "5"}], "}"}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"b", "=", 
   RowBox[{"RandomInteger", "[", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "5"}], ",", "5"}], "}"}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"c", "=", 
   RowBox[{"RandomInteger", "[", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "5"}], ",", "5"}], "}"}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{
   RowBox[{"f", "[", "x", "]"}], ":=", 
   RowBox[{
    RowBox[{"c", " ", 
     RowBox[{"Sin", "[", 
      RowBox[{"a", " ", "x"}], "]"}]}], "+", 
    RowBox[{"d", " ", 
     RowBox[{"Cos", "[", 
      RowBox[{"b", " ", "x"}], "]"}]}]}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{
   RowBox[{"sol", "[", "i", "]"}], "=", 
   RowBox[{"Simplify", "[", 
    RowBox[{
     SubscriptBox["\[PartialD]", "x"], 
     RowBox[{"f", "[", "x", "]"}]}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"Print", "[", 
   RowBox[{"i", ",", "\"\<)  f(x) = \>\"", ",", 
    RowBox[{"f", "[", "x", "]"}]}], "]"}], ";"}]}], "Input",
 CellOpen->False,
 FontColor->RGBColor[0, 0.500999, 0.500999]],

Cell[BoxData[
 FormBox[
  InterpretationBox[
   RowBox[{
   "10", "\[InvisibleSpace]", "\<\")  f(x) = \"\>", "\[InvisibleSpace]", 
    RowBox[{
     RowBox[{
      RowBox[{"-", "3"}], " ", 
      RowBox[{"cos", "(", "x", ")"}]}], "-", 
     RowBox[{"2", " ", 
      RowBox[{"sin", "(", 
       RowBox[{"4", " ", "x"}], ")"}]}]}]}],
   SequenceForm[
   10, ")  f(x) = ", (-3) Cos[$CellContext`x] - 2 Sin[4 $CellContext`x]],
   Editable->False], TraditionalForm]], "Print",
 CellChangeTimes->{{3.398430849157301*^9, 3.398430874074911*^9}, 
   3.3984309783032*^9, {3.398431235681219*^9, 3.398431257815654*^9}},
 FontColor->RGBColor[0, 0.500999, 0.500999]]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Solutions :", "Subsection",
 FontColor->RGBColor[0.501961, 0, 0]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Do", "[", 
  RowBox[{
   RowBox[{"Print", "[", 
    RowBox[{"i", ",", "\"\<) f'(x) = \>\"", ",", 
     RowBox[{"sol", "[", "i", "]"}]}], "]"}], ",", 
   RowBox[{"{", 
    RowBox[{"i", ",", "1", ",", "10"}], "}"}]}], "]"}]], "Input",
 CellOpen->False,
 FontColor->RGBColor[0, 0.500999, 0.500999]],

Cell[CellGroupData[{

Cell[BoxData[
 FormBox[
  InterpretationBox[
   RowBox[{
   "1", "\[InvisibleSpace]", "\<\") f'(x) = \"\>", "\[InvisibleSpace]", 
    FractionBox[
     RowBox[{
      RowBox[{"10", " ", "x"}], "-", "3"}], 
     RowBox[{"2", " ", 
      SqrtBox[
       RowBox[{
        RowBox[{"5", " ", 
         SuperscriptBox["x", "2"]}], "-", 
        RowBox[{"3", " ", "x"}], "+", "2"}]]}]]}],
   SequenceForm[
   1, ") f'(x) = ", 
    Rational[1, 2] (-3 + 
     10 $CellContext`x) (2 - 3 $CellContext`x + 5 $CellContext`x^2)^
     Rational[-1, 2]],
   Editable->False], TraditionalForm]], "Print",
 CellChangeTimes->{3.3984308931051826`*^9, 3.39843098514224*^9, 
  3.3984310421682653`*^9, 3.398431155706727*^9, 3.398431268796197*^9},
 FontColor->RGBColor[0, 0.500999, 0.500999]],

Cell[BoxData[
 FormBox[
  InterpretationBox[
   RowBox[{
   "2", "\[InvisibleSpace]", "\<\") f'(x) = \"\>", "\[InvisibleSpace]", 
    RowBox[{"20", " ", "x", " ", 
     RowBox[{"(", 
      RowBox[{
       RowBox[{"5", " ", 
        SuperscriptBox["x", "2"]}], "-", "8"}], ")"}]}]}],
   SequenceForm[2, ") f'(x) = ", 20 $CellContext`x (-8 + 5 $CellContext`x^2)],
   
   Editable->False], TraditionalForm]], "Print",
 CellChangeTimes->{3.3984308931051826`*^9, 3.39843098514224*^9, 
  3.3984310421682653`*^9, 3.398431155706727*^9, 3.39843126879851*^9},
 FontColor->RGBColor[0, 0.500999, 0.500999]],

Cell[BoxData[
 FormBox[
  InterpretationBox[
   RowBox[{
   "3", "\[InvisibleSpace]", "\<\") f'(x) = \"\>", "\[InvisibleSpace]", 
    RowBox[{
     RowBox[{"3", " ", 
      RowBox[{"sin", "(", "x", ")"}]}], "-", 
     RowBox[{"8", " ", 
      RowBox[{"cos", "(", 
       RowBox[{"4", " ", "x"}], ")"}]}]}]}],
   SequenceForm[
   3, ") f'(x) = ", (-8) Cos[4 $CellContext`x] + 3 Sin[$CellContext`x]],
   Editable->False], TraditionalForm]], "Print",
 CellChangeTimes->{3.3984308931051826`*^9, 3.39843098514224*^9, 
  3.3984310421682653`*^9, 3.398431155706727*^9, 3.3984312688024387`*^9},
 FontColor->RGBColor[0, 0.500999, 0.500999]],

Cell[BoxData[
 FormBox[
  InterpretationBox[
   RowBox[{
   "4", "\[InvisibleSpace]", "\<\") f'(x) = \"\>", "\[InvisibleSpace]", 
    RowBox[{
     RowBox[{"-", "4"}], " ", "x", " ", 
     RowBox[{"cos", "(", 
      RowBox[{"1", "-", 
       RowBox[{"2", " ", 
        SuperscriptBox["x", "2"]}]}], ")"}]}]}],
   SequenceForm[
   4, ") f'(x) = ", (-4) $CellContext`x Cos[1 - 2 $CellContext`x^2]],
   Editable->False], TraditionalForm]], "Print",
 CellChangeTimes->{3.3984308931051826`*^9, 3.39843098514224*^9, 
  3.3984310421682653`*^9, 3.398431155706727*^9, 3.398431268804119*^9},
 FontColor->RGBColor[0, 0.500999, 0.500999]],

Cell[BoxData[
 FormBox[
  InterpretationBox[
   RowBox[{
   "5", "\[InvisibleSpace]", "\<\") f'(x) = \"\>", "\[InvisibleSpace]", 
    RowBox[{"3", " ", 
     RowBox[{"cos", "(", "x", ")"}], " ", 
     RowBox[{
      SuperscriptBox["sin", "2"], "(", "x", ")"}]}]}],
   SequenceForm[5, ") f'(x) = ", 3 Cos[$CellContext`x] Sin[$CellContext`x]^2],
   
   Editable->False], TraditionalForm]], "Print",
 CellChangeTimes->{3.3984308931051826`*^9, 3.39843098514224*^9, 
  3.3984310421682653`*^9, 3.398431155706727*^9, 3.3984312688058023`*^9},
 FontColor->RGBColor[0, 0.500999, 0.500999]],

Cell[BoxData[
 FormBox[
  InterpretationBox[
   RowBox[{
   "6", "\[InvisibleSpace]", "\<\") f'(x) = \"\>", "\[InvisibleSpace]", 
    RowBox[{"-", 
     FractionBox[
      RowBox[{"sin", "(", 
       SqrtBox["x"], ")"}], 
      RowBox[{"2", " ", 
       SqrtBox["x"]}]]}]}],
   SequenceForm[
   6, ") f'(x) = ", Rational[-1, 2] $CellContext`x^Rational[-1, 2] 
    Sin[$CellContext`x^Rational[1, 2]]],
   Editable->False], TraditionalForm]], "Print",
 CellChangeTimes->{3.3984308931051826`*^9, 3.39843098514224*^9, 
  3.3984310421682653`*^9, 3.398431155706727*^9, 3.398431268807479*^9},
 FontColor->RGBColor[0, 0.500999, 0.500999]],

Cell[BoxData[
 FormBox[
  InterpretationBox[
   RowBox[{
   "7", "\[InvisibleSpace]", "\<\") f'(x) = \"\>", "\[InvisibleSpace]", 
    RowBox[{"-", 
     FractionBox[
      RowBox[{"cos", "(", 
       FractionBox["1", "x"], ")"}], 
      SuperscriptBox["x", "2"]]}]}],
   SequenceForm[
   7, ") f'(x) = ", -$CellContext`x^(-2) Cos[$CellContext`x^(-1)]],
   Editable->False], TraditionalForm]], "Print",
 CellChangeTimes->{3.3984308931051826`*^9, 3.39843098514224*^9, 
  3.3984310421682653`*^9, 3.398431155706727*^9, 3.3984312688093*^9},
 FontColor->RGBColor[0, 0.500999, 0.500999]],

Cell[BoxData[
 FormBox[
  InterpretationBox[
   RowBox[{
   "8", "\[InvisibleSpace]", "\<\") f'(x) = \"\>", "\[InvisibleSpace]", 
    RowBox[{
     RowBox[{"2", " ", 
      RowBox[{"cos", "(", 
       RowBox[{"4", " ", "x"}], ")"}]}], "-", 
     RowBox[{"cos", "(", 
      RowBox[{"2", " ", "x"}], ")"}]}]}],
   SequenceForm[
   8, ") f'(x) = ", -Cos[2 $CellContext`x] + 2 Cos[4 $CellContext`x]],
   Editable->False], TraditionalForm]], "Print",
 CellChangeTimes->{3.3984308931051826`*^9, 3.39843098514224*^9, 
  3.3984310421682653`*^9, 3.398431155706727*^9, 3.398431268811145*^9},
 FontColor->RGBColor[0, 0.500999, 0.500999]],

Cell[BoxData[
 FormBox[
  InterpretationBox[
   RowBox[{
   "9", "\[InvisibleSpace]", "\<\") f'(x) = \"\>", "\[InvisibleSpace]", 
    RowBox[{"-", 
     FractionBox[
      RowBox[{"2", " ", 
       RowBox[{"cos", "(", 
        FractionBox["x", 
         RowBox[{"x", "-", "2"}]], ")"}]}], 
      SuperscriptBox[
       RowBox[{"(", 
        RowBox[{"x", "-", "2"}], ")"}], "2"]]}]}],
   SequenceForm[
   9, ") f'(x) = ", (-2) (-2 + $CellContext`x)^(-2) 
    Cos[(-2 + $CellContext`x)^(-1) $CellContext`x]],
   Editable->False], TraditionalForm]], "Print",
 CellChangeTimes->{3.3984308931051826`*^9, 3.39843098514224*^9, 
  3.3984310421682653`*^9, 3.398431155706727*^9, 3.398431268812834*^9},
 FontColor->RGBColor[0, 0.500999, 0.500999]],

Cell[BoxData[
 FormBox[
  InterpretationBox[
   RowBox[{
   "10", "\[InvisibleSpace]", "\<\") f'(x) = \"\>", "\[InvisibleSpace]", 
    RowBox[{
     RowBox[{"3", " ", 
      RowBox[{"sin", "(", "x", ")"}]}], "-", 
     RowBox[{"8", " ", 
      RowBox[{"cos", "(", 
       RowBox[{"4", " ", "x"}], ")"}]}]}]}],
   SequenceForm[
   10, ") f'(x) = ", (-8) Cos[4 $CellContext`x] + 3 Sin[$CellContext`x]],
   Editable->False], TraditionalForm]], "Print",
 CellChangeTimes->{3.3984308931051826`*^9, 3.39843098514224*^9, 
  3.3984310421682653`*^9, 3.398431155706727*^9, 3.3984312688435087`*^9},
 FontColor->RGBColor[0, 0.500999, 0.500999]]
}, Open  ]]
}, Open  ]]
}, Open  ]]
}, Open  ]]
},
WindowSize->{853, 818},
WindowMargins->{{11, Automatic}, {Automatic, 54}},
DockedCells->(FrontEndExecute[{
   FrontEnd`NotebookApply[
    FrontEnd`InputNotebook[], #, Placeholder]}]& ),
PrintingCopies->1,
PrintingPageRange->{1, Automatic},
CellLabelAutoDelete->True,
FrontEndVersion->"6.0 for Mac OS X x86 (32-bit) (June 19, 2007)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[590, 23, 200, 4, 67, "Section"],
Cell[CellGroupData[{
Cell[815, 31, 107, 3, 34, "Subsection"],
Cell[CellGroupData[{
Cell[947, 38, 1309, 44, 19, "Input",
 CellOpen->False],
Cell[2259, 84, 610, 17, 31, "Print"]
}, Open  ]],
Cell[CellGroupData[{
Cell[2906, 106, 1325, 45, 19, "Input",
 CellOpen->False],
Cell[4234, 153, 566, 15, 30, "Print"]
}, Open  ]],
Cell[CellGroupData[{
Cell[4837, 173, 835, 27, 19, "Input",
 CellOpen->False],
Cell[5675, 202, 590, 15, 44, "Print"]
}, Open  ]],
Cell[CellGroupData[{
Cell[6302, 222, 834, 26, 19, "Input",
 CellOpen->False],
Cell[7139, 250, 597, 15, 28, "Print"]
}, Open  ]],
Cell[CellGroupData[{
Cell[7773, 270, 786, 24, 20, "Input",
 CellOpen->False],
Cell[8562, 296, 559, 12, 25, "Print"]
}, Open  ]],
Cell[CellGroupData[{
Cell[9158, 313, 1378, 45, 20, "Input",
 CellOpen->False],
Cell[10539, 360, 494, 13, 37, "Print"]
}, Open  ]],
Cell[CellGroupData[{
Cell[11070, 378, 1390, 46, 20, "Input",
 CellOpen->False],
Cell[12463, 426, 493, 13, 40, "Print"]
}, Open  ]],
Cell[CellGroupData[{
Cell[12993, 444, 823, 25, 20, "Input",
 CellOpen->False],
Cell[13819, 471, 567, 14, 23, "Print"]
}, Open  ]],
Cell[CellGroupData[{
Cell[14423, 490, 1441, 48, 20, "Input",
 CellOpen->False],
Cell[15867, 540, 536, 14, 38, "Print"]
}, Open  ]],
Cell[CellGroupData[{
Cell[16440, 559, 1313, 45, 20, "Input",
 CellOpen->False],
Cell[17756, 606, 652, 17, 23, "Print"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[18457, 629, 71, 1, 34, "Subsection"],
Cell[CellGroupData[{
Cell[18553, 634, 319, 9, 20, "Input",
 CellOpen->False],
Cell[CellGroupData[{
Cell[18897, 647, 767, 22, 50, "Print"],
Cell[19667, 671, 594, 15, 28, "Print"],
Cell[20264, 688, 630, 16, 23, "Print"],
Cell[20897, 706, 626, 16, 28, "Print"],
Cell[21526, 724, 579, 14, 25, "Print"],
Cell[22108, 740, 630, 17, 49, "Print"],
Cell[22741, 759, 580, 15, 51, "Print"],
Cell[23324, 776, 626, 16, 23, "Print"],
Cell[23953, 794, 736, 20, 53, "Print"],
Cell[24692, 816, 632, 16, 23, "Print"]
}, Open  ]]
}, Open  ]]
}, Open  ]]
}, Open  ]]
}
]
*)

(* End of internal cache information *)