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

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

(* CreatedBy='Mathematica 12.1' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       158,          7]
NotebookDataLength[      6393,        186]
NotebookOptionsPosition[      4996,        156]
NotebookOutlinePosition[      5438,        174]
CellTagsIndexPosition[      5395,        171]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell[BoxData[{
 RowBox[{"\[Rho]", "=", 
  RowBox[{"Sqrt", "[", 
   RowBox[{
    RowBox[{"x", "^", "2"}], "+", 
    RowBox[{"y", "^", "2"}]}], "]"}]}], "\[IndentingNewLine]", 
 RowBox[{"\[Rho]dx", "=", 
  RowBox[{"D", "[", 
   RowBox[{"\[Rho]", ",", "x"}], "]"}]}], "\[IndentingNewLine]", 
 RowBox[{"\[Rho]dy", "=", 
  RowBox[{"D", "[", 
   RowBox[{"\[Rho]", ",", "y"}], "]"}]}], "\[IndentingNewLine]", 
 RowBox[{"\[Theta]", "=", 
  RowBox[{"ArcTan", "[", 
   RowBox[{"y", "/", "x"}], "]"}]}], "\[IndentingNewLine]", 
 RowBox[{"\[Theta]dx", "=", 
  RowBox[{"D", "[", 
   RowBox[{"\[Theta]", ",", "x"}], "]"}]}], "\[IndentingNewLine]", 
 RowBox[{"\[Theta]dy", "=", 
  RowBox[{"D", "[", 
   RowBox[{"\[Theta]", ",", "y"}], "]"}]}], "\[IndentingNewLine]"}], "Input",
 CellChangeTimes->{{3.8784382658192835`*^9, 3.878438318023821*^9}, {
  3.878438382060782*^9, 3.8784384445078783`*^9}, {3.878438692212818*^9, 
  3.878438788628728*^9}},ExpressionUUID->"4dfbf8ed-9005-4c2b-851d-\
8155f964c7c7"],

Cell[BoxData[
 SqrtBox[
  RowBox[{
   SuperscriptBox["x", "2"], "+", 
   SuperscriptBox["y", "2"]}]]], "Output",
 CellChangeTimes->{3.8784383202187033`*^9, 3.8784383880180416`*^9, 
  3.878438445949034*^9, 3.878438748224347*^9},
 CellLabel->"Out[96]=",ExpressionUUID->"1e3abc25-3e1e-4232-b034-08d32cee6940"],

Cell[BoxData[
 FractionBox["x", 
  SqrtBox[
   RowBox[{
    SuperscriptBox["x", "2"], "+", 
    SuperscriptBox["y", "2"]}]]]], "Output",
 CellChangeTimes->{3.8784383202187033`*^9, 3.8784383880180416`*^9, 
  3.878438445949034*^9, 3.878438748229962*^9},
 CellLabel->"Out[97]=",ExpressionUUID->"ee01428f-b688-42e7-a071-76d9244634cc"],

Cell[BoxData[
 FractionBox["y", 
  SqrtBox[
   RowBox[{
    SuperscriptBox["x", "2"], "+", 
    SuperscriptBox["y", "2"]}]]]], "Output",
 CellChangeTimes->{3.8784383202187033`*^9, 3.8784383880180416`*^9, 
  3.878438445949034*^9, 3.878438748234679*^9},
 CellLabel->"Out[98]=",ExpressionUUID->"bb56266c-c2e4-49c9-bf88-462d98e3fd96"],

Cell[BoxData[
 RowBox[{"ArcTan", "[", 
  FractionBox["y", "x"], "]"}]], "Output",
 CellChangeTimes->{3.8784383202187033`*^9, 3.8784383880180416`*^9, 
  3.878438445949034*^9, 3.878438748237789*^9},
 CellLabel->"Out[99]=",ExpressionUUID->"a527bf73-6940-48ad-a75c-49e36d57ed95"],

Cell[BoxData[
 RowBox[{"-", 
  FractionBox["y", 
   RowBox[{
    SuperscriptBox["x", "2"], " ", 
    RowBox[{"(", 
     RowBox[{"1", "+", 
      FractionBox[
       SuperscriptBox["y", "2"], 
       SuperscriptBox["x", "2"]]}], ")"}]}]]}]], "Output",
 CellChangeTimes->{3.8784383202187033`*^9, 3.8784383880180416`*^9, 
  3.878438445949034*^9, 3.878438748240732*^9},
 CellLabel->
  "Out[100]=",ExpressionUUID->"053938a7-f802-48a1-9a01-e191547e3610"],

Cell[BoxData[
 FractionBox["1", 
  RowBox[{"x", " ", 
   RowBox[{"(", 
    RowBox[{"1", "+", 
     FractionBox[
      SuperscriptBox["y", "2"], 
      SuperscriptBox["x", "2"]]}], ")"}]}]]], "Output",
 CellChangeTimes->{3.8784383202187033`*^9, 3.8784383880180416`*^9, 
  3.878438445949034*^9, 3.8784387482436876`*^9},
 CellLabel->
  "Out[101]=",ExpressionUUID->"ccf6eebc-9c3b-4c22-82d1-6a65d9306210"],

Cell[BoxData[
 RowBox[{"Hold", "[", 
  FractionBox[
   SqrtBox[
    RowBox[{
     SuperscriptBox["x", "2"], "+", 
     SuperscriptBox["y", "2"]}]], 
   SqrtBox[
    RowBox[{"1", "+", 
     FractionBox[
      SuperscriptBox["y", "2"], 
      SuperscriptBox["x", "2"]]}]]], "]"}]], "Output",
 CellChangeTimes->{3.8784383202187033`*^9, 3.8784383880180416`*^9, 
  3.878438445949034*^9, 3.8784387482466793`*^9},
 CellLabel->
  "Out[102]=",ExpressionUUID->"cdc86209-c42c-49e6-ba6a-e98b0ead8b40"],

Cell[BoxData[
 RowBox[{"Hold", "[", 
  RowBox[{"y", "=", 
   RowBox[{"\[Rho]", " ", 
    RowBox[{"Sin", "[", "\[Theta]", "]"}]}]}], "]"}]], "Output",
 CellChangeTimes->{3.8784383202187033`*^9, 3.8784383880180416`*^9, 
  3.878438445949034*^9, 3.8784387482506766`*^9},
 CellLabel->
  "Out[103]=",ExpressionUUID->"3525b2a9-f8d4-465f-a821-eab76b0da3e5"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"ReleaseHold", "[", "y", "]"}]], "Input",
 NumberMarks->False,
 CellLabel->
  "In[108]:=",ExpressionUUID->"52538120-62a7-4382-89c2-7e9def520f4c"],

Cell[BoxData["y"], "Output",
 CellChangeTimes->{
  3.8784383202187033`*^9, 3.8784383880180416`*^9, 3.878438445949034*^9, {
   3.878438748254642*^9, 3.878438765517658*^9}},
 CellLabel->
  "Out[108]=",ExpressionUUID->"4d08bf64-aa6e-41a9-8bb8-b850f12ea9b0"]
}, Open  ]]
},
WindowSize->{820, 833},
WindowMargins->{{78, Automatic}, {40, Automatic}},
Magnification:>1.5 Inherited,
FrontEndVersion->"12.1 for Microsoft Windows (64-bit) (2020\:5e743\:670814\
\:65e5)",
StyleDefinitions->"Default.nb",
ExpressionUUID->"1e91df61-5a9f-457b-a3d9-d1151d794321"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[580, 22, 987, 24, 368, "Input",ExpressionUUID->"4dfbf8ed-9005-4c2b-851d-8155f964c7c7"],
Cell[1570, 48, 306, 7, 53, "Output",ExpressionUUID->"1e3abc25-3e1e-4232-b034-08d32cee6940"],
Cell[1879, 57, 330, 8, 75, "Output",ExpressionUUID->"ee01428f-b688-42e7-a071-76d9244634cc"],
Cell[2212, 67, 330, 8, 75, "Output",ExpressionUUID->"bb56266c-c2e4-49c9-bf88-462d98e3fd96"],
Cell[2545, 77, 275, 5, 66, "Output",ExpressionUUID->"a527bf73-6940-48ad-a75c-49e36d57ed95"],
Cell[2823, 84, 448, 13, 88, "Output",ExpressionUUID->"053938a7-f802-48a1-9a01-e191547e3610"],
Cell[3274, 99, 400, 11, 91, "Output",ExpressionUUID->"ccf6eebc-9c3b-4c22-82d1-6a65d9306210"],
Cell[3677, 112, 489, 15, 101, "Output",ExpressionUUID->"cdc86209-c42c-49e6-ba6a-e98b0ead8b40"],
Cell[4169, 129, 349, 8, 49, "Output",ExpressionUUID->"3525b2a9-f8d4-465f-a821-eab76b0da3e5"]
}, Open  ]],
Cell[CellGroupData[{
Cell[4555, 142, 168, 4, 66, "Input",ExpressionUUID->"52538120-62a7-4382-89c2-7e9def520f4c"],
Cell[4726, 148, 254, 5, 49, "Output",ExpressionUUID->"4d08bf64-aa6e-41a9-8bb8-b850f12ea9b0"]
}, Open  ]]
}
]
*)