DLMF:1.6.E20 (Q172): Difference between revisions

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Property / Digital Library of Mathematical Functions ID
 
Property / Digital Library of Mathematical Functions ID: DLMF:1.6.E20 / rank
Normal rank
 
Property / Digital Library of Mathematical Functions ID
 
Property / Digital Library of Mathematical Functions ID: 1.6.E20 / rank
 
Normal rank
Property / Symbols defined
 
Property / Symbols defined: gradient of differentiable scalar function / rank
 
Normal rank
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
 
DLMF 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.m4aadec
Property / Symbols used
 
Property / Symbols used: partial differential of $$x$$ / rank
 
Normal rank
Property / Symbols used: partial differential of $$x$$ / qualifier
 
DLMF 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.m2aadec
Property / Symbols used
 
Property / Symbols used: variable / rank
 
Normal rank
Property / Symbols used: variable / qualifier
 
DLMF defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: variable / qualifier
 
xml-id: C1.S1.XMD1.m1adec
Property / Symbols used
 
Property / Symbols used: unit vector / rank
 
Normal rank
Property / Symbols used: unit vector / qualifier
 
DLMF defining formula:

𝐢 𝐢 {\displaystyle{\displaystyle\mathbf{i}}}

\mathbf{i}
Property / Symbols used: unit vector / qualifier
 
xml-id: C1.S6.XMD2.m1fdec
Property / Symbols used
 
Property / Symbols used: unit vector / rank
 
Normal rank
Property / Symbols used: unit vector / qualifier
 
DLMF defining formula:

𝐣 𝐣 {\displaystyle{\displaystyle\mathbf{j}}}

\mathbf{j}
Property / Symbols used: unit vector / qualifier
 
xml-id: C1.S6.XMD3.m1fdec
Property / Symbols used
 
Property / Symbols used: unit vector / rank
 
Normal rank
Property / Symbols used: unit vector / qualifier
 
DLMF defining formula:

𝐤 𝐤 {\displaystyle{\displaystyle\mathbf{k}}}

\mathbf{k}
Property / Symbols used: unit vector / qualifier
 
xml-id: C1.S6.XMD4.m1fdec
Property / instance of
 
Property / instance of: Digital Library of Mathematical Functions Formula / rank
 
Normal rank
Property / MaRDI profile type
 
Property / MaRDI profile type: MaRDI formula profile / rank
 
Normal rank
links / mardi / namelinks / mardi / name
 

Latest revision as of 01:29, 3 March 2024

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DLMF:1.6.E20
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    Statements

    grad f = f = f x 𝐢 + f y 𝐣 + f z 𝐤 . 𝑓 𝑓 partial-derivative 𝑓 𝑥 𝐢 partial-derivative 𝑓 𝑦 𝐣 partial-derivative 𝑓 𝑧 𝐤 {\displaystyle{\displaystyle\operatorname{grad}f=\nabla f=\frac{\partial f}{% \partial x}\mathbf{i}+\frac{\partial f}{\partial y}\mathbf{j}+\frac{\partial f% }{\partial z}\mathbf{k}.}}
    0 references
    f x partial-derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}
    C1.S5.E3.m4aadec
    0 references
    x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}
    C1.S5.E3.m2aadec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C1.S1.XMD1.m1adec
    0 references
    𝐢 𝐢 {\displaystyle{\displaystyle\mathbf{i}}}
    C1.S6.XMD2.m1fdec
    0 references
    𝐣 𝐣 {\displaystyle{\displaystyle\mathbf{j}}}
    C1.S6.XMD3.m1fdec
    0 references
    𝐤 𝐤 {\displaystyle{\displaystyle\mathbf{k}}}
    C1.S6.XMD4.m1fdec
    0 references

    Identifiers