D[Csch[z], {z, 2}] == Csch[z] (Coth[z]^2 + Csch[z]^2)

Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["{", RowBox[List["z", ",", "2"]], "}"]]], RowBox[List["Csch", "[", "z", "]"]]]], "\[Equal]", RowBox[List[RowBox[List["Csch", "[", "z", "]"]], " ", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["Coth", "[", "z", "]"]], "2"], "+", SuperscriptBox[RowBox[List["Csch", "[", "z", "]"]], "2"]]], ")"]]]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mfrac> <mrow> <msup> <mo> &#8706; </mo> <mn> 2 </mn> </msup> <mrow> <mi> csch </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> &#10869; </mo> <mrow> <mrow> <mi> csch </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> coth </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <msup> <mi> csch </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <cn type='integer'> 2 </cn> </degree> </bvar> <apply> <csch /> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <csch /> <ci> z </ci> </apply> <apply> <plus /> <apply> <power /> <apply> <coth /> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <csch /> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["z_", ",", "2"]], "}"]]]]], RowBox[List["Csch", "[", "z_", "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Csch", "[", "z", "]"]], " ", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["Coth", "[", "z", "]"]], "2"], "+", SuperscriptBox[RowBox[List["Csch", "[", "z", "]"]], "2"]]], ")"]]]]]]]]

2001-10-29