DLMF:1.5.E11 (Q130): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: cosine function / rank
 
Normal rank
Property / Symbols used: cosine function / qualifier
 
Defining formula:

cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}

\cos@@{\NVar{z}}
Property / Symbols used: cosine function / qualifier
 
xml-id: C4.S14.E2.m2aadec
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.m4afdec
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
Property / Symbols used
 
Property / Symbols used: sine function / rank
 
Normal rank
Property / Symbols used: sine function / qualifier
 
Defining formula:

sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}

\sin@@{\NVar{z}}
Property / Symbols used: sine function / qualifier
 
xml-id: C4.S14.E1.m2aadec
Property / Symbols used
 
Property / Symbols used: Q10778 / rank
 
Normal rank
Property / Symbols used: Q10778 / qualifier
 
Defining formula:

ϕ italic-ϕ {\displaystyle{\displaystyle\phi}}

\phi
Property / Symbols used: Q10778 / qualifier
 
xml-id: C1.S5.XMD10.m1adec
Property / Symbols used
 
Property / Symbols used: Q10779 / rank
 
Normal rank
Property / Symbols used: Q10779 / qualifier
 
Defining formula:

r 𝑟 {\displaystyle{\displaystyle r}}

r
Property / Symbols used: Q10779 / qualifier
 
xml-id: C1.S5.XMD6.m1adec

Latest revision as of 15:53, 1 January 2020

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DLMF:1.5.E11
No description defined

    Statements

    Defining formula
    ∂ ∂ ⁡ x = cos ⁡ ϕ ⁢ ∂ ∂ ⁡ r - sin ⁡ ϕ r ⁢ ∂ ∂ ⁡ ϕ , partial-derivative 𝑥 italic-ϕ partial-derivative 𝑟 italic-ϕ 𝑟 partial-derivative italic-ϕ {\displaystyle{\displaystyle\frac{\partial}{\partial x}=\cos\phi\frac{\partial% }{\partial r}-\frac{\sin\phi}{r}\frac{\partial}{\partial\phi},}}
    0 references
    DLMF id
    DLMF:1.5.E11
    0 references
    Symbols used
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aadec
    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.m4afdec
    0 references
    partial differential of $$x$$
    Defining formula
    ∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}
    xml-id
    C1.S5.E3.m2agdec
    0 references
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2aadec
    0 references
    Q10778
    Defining formula
    ϕ italic-ϕ {\displaystyle{\displaystyle\phi}}
    xml-id
    C1.S5.XMD10.m1adec
    0 references
    Q10779
    Defining formula
    r 𝑟 {\displaystyle{\displaystyle r}}
    xml-id
    C1.S5.XMD6.m1adec
    0 references
     
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