DLMF:1.4.E13 (Q92): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
test:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5adec
Property / Symbols used
 
Property / Symbols used: Q10756 / rank
 
Normal rank
Property / Symbols used: Q10756 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q10756 / qualifier
 
xml-id: C1.S1.XMD4.m1adec
Property / Symbols used
 
Property / Symbols used: Q10761 / rank
 
Normal rank
Property / Symbols used: Q10761 / qualifier
 
test:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q10761 / qualifier
 
xml-id: C1.S1.XMD6.m1dec
Property / Symbols used
 
Property / Symbols used: Q10757 / rank
 
Normal rank
Property / Symbols used: Q10757 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q10757 / qualifier
 
xml-id: C1.S1.XMD7.m1bdec

Latest revision as of 14:50, 1 January 2020

No description defined
Language Label Description Also known as
English
DLMF:1.4.E13
No description defined

    Statements

    test
    d n d x n ⁡ f ⁢ ( g ⁢ ( x ) ) = ∑ ( n ! m 1 ! ⁢ m 2 ! ⁢ ⋯ ⁢ m n ! ) ⁢ f ( k ) ⁢ ( g ⁢ ( x ) ) ⁢ ( g ′ ⁢ ( x ) 1 ! ) m 1 ⁢ ( g ′′ ⁢ ( x ) 2 ! ) m 2 ⁢ … ⁢ ( g ( n ) ⁢ ( x ) n ! ) m n , derivative 𝑥 𝑛 𝑓 𝑔 𝑥 𝑛 subscript 𝑚 1 subscript 𝑚 2 ⋯ subscript 𝑚 𝑛 superscript 𝑓 𝑘 𝑔 𝑥 superscript superscript 𝑔 ′ 𝑥 1 subscript 𝑚 1 superscript superscript 𝑔 ′′ 𝑥 2 subscript 𝑚 2 … superscript superscript 𝑔 𝑛 𝑥 𝑛 subscript 𝑚 𝑛 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}x}^{n}}f(g(x))=% \sum\left(\frac{n!}{m_{1}!m_{2}!\cdots m_{n}!}\right)f^{(k)}(g(x))\*\left(% \frac{g^{\prime}(x)}{1!}\right)^{m_{1}}\left(\frac{g^{\prime\prime}(x)}{2!}% \right)^{m_{2}}\dots\left(\frac{g^{(n)}(x)}{n!}\right)^{m_{n}},}}
    0 references
    DLMF id
    DLMF:1.4.E13
    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.m2acdec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
    0 references
    Q10756
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C1.S1.XMD4.m1adec
    0 references
    Q10761
    test
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C1.S1.XMD6.m1dec
    0 references
    Q10757
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C1.S1.XMD7.m1bdec
    0 references
     
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