(* 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[      5265,        189]
NotebookOptionsPosition[      4816,        171]
NotebookOutlinePosition[      5162,        186]
CellTagsIndexPosition[      5119,        183]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[{"\"\< #34 \>\"", "\[IndentingNewLine]", 
 RowBox[{"D", "[", "   ", 
  RowBox[{
   RowBox[{
    RowBox[{"Cosh", "[", 
     RowBox[{"Sqrt", "[", "z", "]"}], "]"}], "*", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{"Sinh", "[", 
       RowBox[{
        RowBox[{"x", "^", "2"}], "*", "y", "*", "z"}], "]"}], ")"}], "^", 
     "2"}]}], ",", " ", "x"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{"D", "[", "   ", 
  RowBox[{
   RowBox[{
    RowBox[{"Cosh", "[", 
     RowBox[{"Sqrt", "[", "z", "]"}], "]"}], "*", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{"Sinh", "[", 
       RowBox[{
        RowBox[{"x", "^", "2"}], "*", "y", "*", "z"}], "]"}], ")"}], "^", 
     "2"}]}], ",", " ", "y"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{"D", "[", "   ", 
  RowBox[{
   RowBox[{
    RowBox[{"Cosh", "[", 
     RowBox[{"Sqrt", "[", "z", "]"}], "]"}], "*", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{"Sinh", "[", 
       RowBox[{
        RowBox[{"x", "^", "2"}], "*", "y", "*", "z"}], "]"}], ")"}], "^", 
     "2"}]}], ",", " ", "z"}], "]"}]}], "Input"],

Cell[BoxData[{"\"\< #57 \>\"", "\[IndentingNewLine]", 
 RowBox[{"D", "[", "  ", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"(", 
      RowBox[{
       RowBox[{"x", "^", "2"}], "+", 
       RowBox[{"y", "^", "2"}], "+", 
       RowBox[{"z", "^", "2"}]}], ")"}], "^", 
     RowBox[{"(", 
      RowBox[{"3", "/", "2"}], ")"}]}], "-", "1"}], ",", "  ", "x", ",", 
   "   ", 
   RowBox[{"NonConstants", "\[Rule]", 
    RowBox[{"{", "z", "}"}]}]}], "    ", "]"}]}], "Input"],

Cell[BoxData[{"\"\< #66 \>\"", "\[IndentingNewLine]", 
 RowBox[{"D", "[", "   ", 
  RowBox[{
   RowBox[{"Integrate", "[", 
    RowBox[{
     RowBox[{"Exp", "[", 
      RowBox[{"t", "^", "2"}], "]"}], ",", 
     RowBox[{"{", 
      RowBox[{"t", ",", "1", ",", 
       RowBox[{"x", "*", "y"}]}], "}"}]}], "]"}], ",", " ", "x"}], 
  "]"}]}], "Input"],

Cell[BoxData[{"\"\< #71 \>\"", "\[IndentingNewLine]", 
 RowBox[{"D", "[", "   ", 
  RowBox[{
   RowBox[{
    RowBox[{"Exp", "[", "x", "]"}], "*", 
    RowBox[{"Cos", "[", "y", "]"}]}], ",", " ", "x", ",", "y"}], 
  "]"}], "\[IndentingNewLine]", 
 RowBox[{"D", "[", "   ", 
  RowBox[{
   RowBox[{
    RowBox[{"Exp", "[", "x", "]"}], "*", 
    RowBox[{"Cos", "[", "y", "]"}]}], ",", " ", "y", ",", "x"}], 
  "]"}]}], "Input"],

Cell[BoxData[{"\"\< #81 \>\"", "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"f", "[", 
    RowBox[{"x_", ",", "y_"}], "]"}], ":=", 
   RowBox[{
    RowBox[{"(", 
     RowBox[{"y", "^", "3"}], ")"}], "*", 
    RowBox[{"Exp", "[", 
     RowBox[{
      RowBox[{"-", "5"}], "x"}], "]"}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{"D", "[", " ", 
  RowBox[{
   RowBox[{"f", "[", 
    RowBox[{"x", ",", "y"}], "]"}], ",", " ", "x", ",", "y", ",", "y"}], 
  "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"D", "[", " ", 
   RowBox[{
    RowBox[{"f", "[", 
     RowBox[{"x", ",", "y"}], "]"}], ",", " ", "x", ",", "y", ",", "y"}], 
   "]"}], "/.", 
  RowBox[{"{", 
   RowBox[{
    RowBox[{"x", "\[Rule]", "0"}], ",", 
    RowBox[{"y", "\[Rule]", "1"}]}], "}"}]}]}], "Input"],

Cell[BoxData[{"\"\< #85-a \>\"", "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"z", "[", 
    RowBox[{"x_", ",", "y_"}], "]"}], ":=", 
   RowBox[{
    RowBox[{"x", "^", "2"}], "-", 
    RowBox[{"y", "^", "2"}], "+", 
    RowBox[{"2", "xy"}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  StyleBox[
   SubscriptBox["\[PartialD]", 
    RowBox[{"x", ",", "x"}]],
   FontSize->18], 
  RowBox[{
   StyleBox["z",
    FontSize->18], "[", 
   RowBox[{"x", ",", "y"}], "]"}]}], "\[IndentingNewLine]", 
 RowBox[{
  StyleBox[
   SubscriptBox["\[PartialD]", 
    RowBox[{"y", ",", "y"}]],
   FontSize->18], 
  RowBox[{
   StyleBox["z",
    FontSize->18], "[", 
   RowBox[{"x", ",", "y"}], "]"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   StyleBox[
    SubscriptBox["\[PartialD]", 
     RowBox[{"x", ",", "x"}]],
    FontSize->18], 
   RowBox[{
    StyleBox["z",
     FontSize->18], "[", 
    RowBox[{"x", ",", "y"}], "]"}]}], " ", "+", " ", 
  RowBox[{
   StyleBox[
    SubscriptBox["\[PartialD]", 
     RowBox[{"y", ",", "y"}]],
    FontSize->18], 
   RowBox[{
    StyleBox["z",
     FontSize->18], "[", 
    RowBox[{"x", ",", "y"}], "]"}]}]}]}], "Input"]
},
WindowSize->{1050, 863},
WindowMargins->{{39, Automatic}, {Automatic, 15}},
FrontEndVersion->"7.0 for Microsoft Windows (32-bit) (February 18, 2009)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[545, 20, 1061, 33, 92, "Input"],
Cell[1609, 55, 475, 14, 52, "Input"],
Cell[2087, 71, 347, 10, 52, "Input"],
Cell[2437, 83, 423, 12, 72, "Input"],
Cell[2863, 97, 783, 25, 92, "Input"],
Cell[3649, 124, 1163, 45, 118, "Input"]
}
]
*)

(* End of internal cache information *)