DLMF:4.34.E5 (Q1865): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: hyperbolic tangent function / rank
 
Normal rank
Property / Symbols used: hyperbolic tangent function / qualifier
 
test:

tanh ⁡ z 𝑧 {\displaystyle{\displaystyle\tanh\NVar{z}}}

\tanh@@{\NVar{z}}
Property / Symbols used: hyperbolic tangent function / qualifier
 
xml-id: C4.S28.E4.m2aadec
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.m1ddec

Latest revision as of 18:07, 1 January 2020

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DLMF:4.34.E5
No description defined

    Statements

    test
    d d z ⁡ sech ⁡ z = - sech ⁡ z ⁢ tanh ⁡ z , derivative 𝑧 𝑧 𝑧 𝑧 {\displaystyle{\displaystyle\frac{\mathrm{d}}{\mathrm{d}z}\operatorname{sech}z% =-\operatorname{sech}z\tanh z,}}
    0 references
    DLMF id
    DLMF:4.34.E5
    0 references
    Symbols used
    derivative of $$f$$ with respect to $$x$$
    test
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2addec
    0 references
    hyperbolic secant function
    test
    sech ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{sech}\NVar{z}}}
    xml-id
    C4.S28.E6.m2aadec
    0 references
    hyperbolic tangent function
    test
    tanh ⁡ z 𝑧 {\displaystyle{\displaystyle\tanh\NVar{z}}}
    xml-id
    C4.S28.E4.m2aadec
    0 references
    Q11217
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1ddec
    0 references
     
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