DLMF:4.13.E4 (Q1645): 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.m2adec

Revision as of 17:17, 1 January 2020

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DLMF:4.13.E4
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    Statements

    test
    d W d x = e - W 1 + W , derivative Lambert-W 𝑥 superscript 𝑒 Lambert-W 1 Lambert-W {\displaystyle{\displaystyle\frac{\mathrm{d}W}{\mathrm{d}x}=\frac{e^{-W}}{1+W}% ,}}
    0 references
    DLMF id
    DLMF:4.13.E4
    0 references
    constraint
    x ≠ - 1 e 𝑥 1 𝑒 {\displaystyle{\displaystyle x\neq-\dfrac{1}{e}}}
    0 references
    Symbols used
    Lambert $$W$$ -function
    test
    W ⁡ ( x ) Lambert-W 𝑥 {\displaystyle{\displaystyle W\left(\NVar{x}\right)}}
    xml-id
    C4.S13.E1.m2acdec
    0 references
    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.m2adec
    0 references
     
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