DLMF:1.6.E51 (Q232): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1aidec
Property / Symbols used
 
Property / Symbols used: partial derivative of $$f$$ with respect to $$x$$ / rank
 
Normal rank
Property / Symbols used: partial derivative of $$f$$ with respect to $$x$$ / qualifier
 
test:

∂ ⁡ f ∂ ⁡ x partial-derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}

\pderiv{\NVar{f}}{\NVar{x}}
Property / Symbols used: partial derivative of $$f$$ with respect to $$x$$ / qualifier
 
xml-id: C1.S5.E3.m4ahdec
Property / Symbols used
 
Property / Symbols used: partial differential of $$x$$ / rank
 
Normal rank
Property / Symbols used: partial differential of $$x$$ / qualifier
 
test:

∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}

\pdiff{\NVar{x}}
Property / Symbols used: partial differential of $$x$$ / qualifier
 
xml-id: C1.S5.E3.m2ahdec
Property / Symbols used
 
Property / Symbols used: Q10799 / rank
 
Normal rank
Property / Symbols used: Q10799 / qualifier
 
test:

S 𝑆 {\displaystyle{\displaystyle S}}

S
Property / Symbols used: Q10799 / qualifier
 
xml-id: C1.S6.XMD12.m1adec
Property / Symbols used
 
Property / Symbols used: Q10800 / rank
 
Normal rank
Property / Symbols used: Q10800 / qualifier
 
test:

D 𝐷 {\displaystyle{\displaystyle D}}

D
Property / Symbols used: Q10800 / qualifier
 
xml-id: C1.S6.XMD14.m1adec
Property / Symbols used
 
Property / Symbols used: area of a parameterized smooth surface $$S$$ (locally) / rank
 
Normal rank
Property / Symbols used: area of a parameterized smooth surface $$S$$ (locally) / qualifier
 
test:

A ⁢ ( S ) 𝐴 𝑆 {\displaystyle{\displaystyle A(S)}}

A(S)
Property / Symbols used: area of a parameterized smooth surface $$S$$ (locally) / qualifier
 
xml-id: C1.S6.XMD15.m1adec

Latest revision as of 15:00, 1 January 2020

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DLMF:1.6.E51
No description defined

    Statements

    test
    A ⁢ ( S ) = ∬ D 1 + ( ∂ ⁡ f ∂ ⁡ x ) 2 + ( ∂ ⁡ f ∂ ⁡ y ) 2 ⁢ d A . 𝐴 𝑆 subscript double-integral 𝐷 1 superscript partial-derivative 𝑓 𝑥 2 superscript partial-derivative 𝑓 𝑦 2 𝐴 {\displaystyle{\displaystyle A(S)=\iint_{D}\sqrt{1+\left(\frac{\partial f}{% \partial x}\right)^{2}+\left(\frac{\partial f}{\partial y}\right)^{2}}\mathrm{% d}A.}}
    0 references
    DLMF id
    DLMF:1.6.E51
    0 references
    Symbols used
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aidec
    0 references
    partial derivative of $$f$$ with respect to $$x$$
    test
    ∂ ⁡ f ∂ ⁡ x partial-derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}
    xml-id
    C1.S5.E3.m4ahdec
    0 references
    partial differential of $$x$$
    test
    ∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}
    xml-id
    C1.S5.E3.m2ahdec
    0 references
    Q10799
    test
    S 𝑆 {\displaystyle{\displaystyle S}}
    xml-id
    C1.S6.XMD12.m1adec
    0 references
    Q10800
    test
    D 𝐷 {\displaystyle{\displaystyle D}}
    xml-id
    C1.S6.XMD14.m1adec
    0 references
    area of a parameterized smooth surface $$S$$ (locally)
    test
    A ⁢ ( S ) 𝐴 𝑆 {\displaystyle{\displaystyle A(S)}}
    xml-id
    C1.S6.XMD15.m1adec
    0 references
     
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