DLMF:1.5.E12 (Q131)

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DLMF:1.5.E12
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    Statements

    Defining formula
    ∂ ∂ ⁡ y = sin ⁡ ϕ ⁢ ∂ ∂ ⁡ r + cos ⁡ ϕ r ⁢ ∂ ∂ ⁡ ϕ . partial-derivative 𝑦 italic-ϕ partial-derivative 𝑟 italic-ϕ 𝑟 partial-derivative italic-ϕ {\displaystyle{\displaystyle\frac{\partial}{\partial y}=\sin\phi\frac{\partial% }{\partial r}+\frac{\cos\phi}{r}\frac{\partial}{\partial\phi}.}}
    0 references
    DLMF id
    DLMF:1.5.E12
    0 references
    Symbols used
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2abdec
    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.m2ahdec
    0 references
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2abdec
    0 references
    Q10778
    Defining formula
    ϕ italic-ϕ {\displaystyle{\displaystyle\phi}}
    xml-id
    C1.S5.XMD10.m1bdec
    0 references
    Q10779
    Defining formula
    r 𝑟 {\displaystyle{\displaystyle r}}
    xml-id
    C1.S5.XMD6.m1bdec
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