DLMF:4.38.E13 (Q1963)

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DLMF:4.38.E13
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    Statements

    Defining formula
    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}}.}}
    0 references
    DLMF id
    DLMF:4.38.E13
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    Symbols used
    derivative of $$f$$ with respect to $$x$$
    Defining formula
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2addec
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    inverse hyperbolic secant function
    Defining formula
    arcsech ⁡ z hyperbolic-inverse-secant 𝑧 {\displaystyle{\displaystyle\operatorname{arcsech}\NVar{z}}}
    xml-id
    C4.S37.E8.m2adec
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    Q11217
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1kdec
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