D[ArcTan[x, y], y] == x/(x^2 + y^2)

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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mfrac> <mrow> <mo> &#8706; </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mi> x </mi> <mo> , </mo> <mi> y </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <mi> y </mi> </mrow> </mfrac> <mo> &#10869; </mo> <mfrac> <mi> x </mi> <mrow> <msup> <mi> x </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mi> y </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> y </ci> </bvar> <apply> <arctan /> <ci> x </ci> <ci> y </ci> </apply> </apply> <apply> <times /> <ci> x </ci> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> y </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["y_"]]], RowBox[List["ArcTan", "[", RowBox[List["x_", ",", "y_"]], "]"]]]], "]"]], "\[RuleDelayed]", FractionBox["x", RowBox[List[SuperscriptBox["x", "2"], "+", SuperscriptBox["y", "2"]]]]]]]]

2001-10-29