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 ArcCos

 http://functions.wolfram.com/01.13.13.0004.01

 Input Form

 Sqrt[1 - z^2] Derivative[1][w][z] == -1 /; w[z] == ArcCos[z] && w[0] == Pi/2

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]], RowBox[List[SuperscriptBox["w", "\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]]]], " ", "\[Equal]", RowBox[List["-", "1"]]]], "/;", RowBox[List[RowBox[List[RowBox[List["w", "[", "z", "]"]], "\[Equal]", RowBox[List["ArcCos", "[", "z", "]"]]]], "\[And]", RowBox[List[RowBox[List["w", "[", "0", "]"]], "\[Equal]", FractionBox["\[Pi]", "2"]]]]]]]]]

 MathML Form

 1 - z 2 w ( z ) - 1 /; w ( z ) cos - 1 ( z ) w ( 0 ) π 2 Condition 1 -1 z 2 1 2 z w z -1 w z z w 0 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SqrtBox[RowBox[List["1", "-", SuperscriptBox["z_", "2"]]]], " ", RowBox[List[SuperscriptBox["w", "\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", "1"]], "/;", RowBox[List[RowBox[List[RowBox[List["w", "[", "z", "]"]], "\[Equal]", RowBox[List["ArcCos", "[", "z", "]"]]]], "&&", RowBox[List[RowBox[List["w", "[", "0", "]"]], "\[Equal]", FractionBox["\[Pi]", "2"]]]]]]]]]]]

 Date Added to functions.wolfram.com (modification date)

 2001-10-29