DLMF:32.2.E9 (Q9163): Difference between revisions

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Changed an Item: Add constraint
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
 
Defining formula:

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.m2agdec

Revision as of 13:48, 2 January 2020

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DLMF:32.2.E9
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    Statements

    d 2 u d ζ 2 = 1 u ( d u d ζ ) 2 - 1 ζ d u d ζ + u 2 ( α + γ u ) 4 ζ 2 + β 4 ζ + δ 4 u , derivative 𝑢 𝜁 2 1 𝑢 superscript derivative 𝑢 𝜁 2 1 𝜁 derivative 𝑢 𝜁 superscript 𝑢 2 𝛼 𝛾 𝑢 4 superscript 𝜁 2 𝛽 4 𝜁 𝛿 4 𝑢 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}u}{{\mathrm{d}\zeta}^{2}}=% \frac{1}{u}\left(\frac{\mathrm{d}u}{\mathrm{d}\zeta}\right)^{2}-\frac{1}{\zeta% }\frac{\mathrm{d}u}{\mathrm{d}\zeta}+\frac{u^{2}(\alpha+\gamma u)}{4\zeta^{2}}% +\frac{\beta}{4\zeta}+\frac{\delta}{4u},}}
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    DLMF:32.2.E9
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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.m2agdec
    0 references