DLMF:1.6.E49 (Q230): Difference between revisions

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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
 
Defining formula:

∂ ⁡ 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.m4agdec
Property / Symbols used
 
Property / Symbols used: partial differential of $$x$$ / rank
 
Normal rank
Property / Symbols used: partial differential of $$x$$ / qualifier
 
Defining formula:

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

\pdiff{\NVar{x}}
Property / Symbols used: partial differential of $$x$$ / qualifier
 
xml-id: C1.S5.E3.m2agdec

Latest revision as of 16:00, 1 January 2020

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DLMF:1.6.E49
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    Statements

    Defining formula
    ∥ 𝐓 u × 𝐓 v ∥ = ( ∂ ⁡ ( x , y ) ∂ ⁡ ( u , v ) ) 2 + ( ∂ ⁡ ( y , z ) ∂ ⁡ ( u , v ) ) 2 + ( ∂ ⁡ ( x , z ) ∂ ⁡ ( u , v ) ) 2 . norm subscript 𝐓 𝑢 subscript 𝐓 𝑣 superscript partial-derivative 𝑥 𝑦 𝑢 𝑣 2 superscript partial-derivative 𝑦 𝑧 𝑢 𝑣 2 superscript partial-derivative 𝑥 𝑧 𝑢 𝑣 2 {\displaystyle{\displaystyle\|\mathbf{T}_{u}\times\mathbf{T}_{v}\|=\sqrt{\left% (\frac{\partial(x,y)}{\partial(u,v)}\right)^{2}+\left(\frac{\partial(y,z)}{% \partial(u,v)}\right)^{2}+\left(\frac{\partial(x,z)}{\partial(u,v)}\right)^{2}% }.}}
    0 references
    DLMF id
    DLMF:1.6.E49
    0 references
    Symbols used
    Q10777
    Defining formula
    ( a , b ) 𝑎 𝑏 {\displaystyle{\displaystyle(\NVar{a},\NVar{b})}}
    xml-id
    introduction.Sx4.p1.t1.r29.m6addec
    0 references
    partial derivative of $$f$$ with respect to $$x$$
    Defining formula
    ∂ ⁡ f ∂ ⁡ x partial-derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}
    xml-id
    C1.S5.E3.m4agdec
    0 references
    partial differential of $$x$$
    Defining formula
    ∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}
    xml-id
    C1.S5.E3.m2agdec
    0 references
     
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