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Derivative (multivariable calculus)

In mathematics, the derivative of a function at a point is the linear part of the best affine approximation to the function near the point. In one-variable calculus, this is the tangent line approximation. In multivariable calculus, the same property is generalized to define the derivative of a vector-valued function or function of a vector argument.…

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Derivative as a linear map

Differentials

Total derivative

Chain rule

Total differential equation

Application to equation systems

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Derivative (multivariable calculus)

Nodes60
Edges59
Triples4
Avg. degree1.97
Density0.033333
Components1

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Important terminology

displaystyle derivative total function linear differential isbn derivatives df partial ed approximation example differentiable vector calculus variables also equations respect

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SubjectPredicateObjectConfidenceSrc
thermodynamicsinstance ofwhere the linear approximation lives.In applications0.80text
the language of differentials often has an additional conceptual roleinstance ofwhere the linear approximation lives.In applications0.80text
d Uinstance ofExpressions0.80text
D finstance ofBy expressing the derivative using Jacobian matrices0.80text

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