D[Sign[x], x] == 2 DiracDelta[x]

Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", "x"], RowBox[List["Sign", "[", "x", "]"]]]], "\[Equal]", RowBox[List["2", RowBox[List["DiracDelta", "[", "x", "]"]]]]]]]]

<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> <mi> sgn </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <mi> x </mi> </mrow> </mfrac> <mo> &#10869; </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mi> &#948; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> x </ci> </bvar> <apply> <ci> Sign </ci> <ci> x </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> &#948; </ci> <ci> x </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["x_"]]], RowBox[List["Sign", "[", "x_", "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List["2", " ", RowBox[List["DiracDelta", "[", "x", "]"]]]]]]]]

2001-10-29