DLMF:4.7.E9 (Q1585)

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DLMF:4.7.E9
No description defined

    Statements

    test
    d d z ⁡ a z = a z ⁢ ln ⁡ a , derivative 𝑧 superscript 𝑎 𝑧 superscript 𝑎 𝑧 𝑎 {\displaystyle{\displaystyle\frac{\mathrm{d}}{\mathrm{d}z}a^{z}=a^{z}\ln a,}}
    0 references
    DLMF id
    DLMF:4.7.E9
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    constraint
    a ≠ 0 𝑎 0 {\displaystyle{\displaystyle a\neq 0}}
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    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.m2agdec
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    principal branch of logarithm function
    test
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2abdec
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    Q11221
    test
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C4.S1.XMD4.m1adec
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    Q11217
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1hdec
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