DLMF:4.13.E4 (Q1645): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Lambert $$W$$ -function / rank
 
Normal rank
Property / Symbols used: Lambert $$W$$ -function / qualifier
 
test:

W ( x ) Lambert-W 𝑥 {\displaystyle{\displaystyle W\left(\NVar{x}\right)}}

\LambertW@{\NVar{x}}
Property / Symbols used: Lambert $$W$$ -function / qualifier
 
xml-id: C4.S13.E1.m2acdec
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
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
test:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2addec
Property / Symbols used
 
Property / Symbols used: Q11218 / rank
 
Normal rank
Property / Symbols used: Q11218 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11218 / qualifier
 
xml-id: C4.S1.XMD6.m1cdec

Latest revision as of 17:17, 1 January 2020

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DLMF:4.13.E4
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    Statements

    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}% ,}}
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    x - 1 e 𝑥 1 𝑒 {\displaystyle{\displaystyle x\neq-\dfrac{1}{e}}}
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    W ( x ) Lambert-W 𝑥 {\displaystyle{\displaystyle W\left(\NVar{x}\right)}}
    C4.S13.E1.m2acdec
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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.m2adec
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    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2addec
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    x 𝑥 {\displaystyle{\displaystyle x}}
    C4.S1.XMD6.m1cdec
    0 references