DLMF:4.38.E13 (Q1963): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / rank
 
Normal rank
Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / qualifier
 
test:

d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}

\deriv{\NVar{f}}{\NVar{x}}
Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / qualifier
 
xml-id: C1.S4.E4.m2addec
Property / Symbols used
 
Property / Symbols used: inverse hyperbolic secant function / rank
 
Normal rank
Property / Symbols used: inverse hyperbolic secant function / qualifier
 
test:

arcsech z hyperbolic-inverse-secant 𝑧 {\displaystyle{\displaystyle\operatorname{arcsech}\NVar{z}}}

\asech@@{\NVar{z}}
Property / Symbols used: inverse hyperbolic secant function / qualifier
 
xml-id: C4.S37.E8.m2adec
Property / Symbols used
 
Property / Symbols used: Q11217 / rank
 
Normal rank
Property / Symbols used: Q11217 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11217 / qualifier
 
xml-id: C4.S1.XMD8.m1kdec

Latest revision as of 18:20, 1 January 2020

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DLMF:4.38.E13
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    Statements

    d d z arcsech z = - 1 z ( 1 - z 2 ) 1 / 2 . derivative 𝑧 hyperbolic-inverse-secant 𝑧 1 𝑧 superscript 1 superscript 𝑧 2 1 2 {\displaystyle{\displaystyle\frac{\mathrm{d}}{\mathrm{d}z}\operatorname{% arcsech}z=-\frac{1}{z(1-z^{2})^{1/2}}.}}
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    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    C1.S4.E4.m2addec
    0 references
    arcsech z hyperbolic-inverse-secant 𝑧 {\displaystyle{\displaystyle\operatorname{arcsech}\NVar{z}}}
    C4.S37.E8.m2adec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C4.S1.XMD8.m1kdec
    0 references