Absolute value function: Differentiation (formula 12.01.20.0001)

Abs

$Mathematica Notation$

Complex Components

Abs[z]

Differentiation

Low-order differentiation

http://functions.wolfram.com/12.01.20.0001.01

Input Form

D[Abs[x], x] == Sign[x]

Standard Form

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

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mfrac> <mrow> <mo> ∂ </mo> <mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[LeftBracketingBar]" </annotation> </semantics> <mi> x </mi> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation> </semantics> </mrow> </mrow> <mrow> <mo> ∂ </mo> <mi> x </mi> </mrow> </mfrac> <mo> ⩵ </mo> <mrow> <mi> sgn </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> x </ci> </bvar> <apply> <abs /> <ci> x </ci> </apply> </apply> <apply> <ci> Sign </ci> <ci> x </ci> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

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

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

2001-10-29