D[LogIntegral[z], z] == 1/Log[z]

Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", "z"], RowBox[List["LogIntegral", "[", "z", "]"]]]], "\[Equal]", FractionBox["1", RowBox[List["Log", "[", "z", "]"]]]]]]]

<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> li </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <mi> z </mi> </mrow> </mfrac> <mo> &#10869; </mo> <mfrac> <mn> 1 </mn> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <ci> LogIntegral </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <ln /> <ci> z </ci> </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["z_"]]], RowBox[List["LogIntegral", "[", "z_", "]"]]]], "]"]], "\[RuleDelayed]", FractionBox["1", RowBox[List["Log", "[", "z", "]"]]]]]]]

2001-10-29