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The inverse of differentiation is [[integration]]. |
The inverse of differentiation is [[integration]]. |
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+ | ==Multivariable extensions== |
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+ | For multivariable scalar fields, either a [[:w:c:math:gradient|gradient]] (a [[:w:c:math:vector field|vector field]] representing the direction of greatest change) or [[:w:c:math:directional derivative|directional derivative]] (a scalar representing the rate of change in a particular direction) can be taken. The two equivalents to derivation over a scalar field are [[:w:c:math:divergence|divergence]] and [[:w:c:math:curl|curl]]. |
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==Derivatives in physics== |
==Derivatives in physics== |
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:<math>W'(d) = F(d)</math> |
:<math>W'(d) = F(d)</math> |
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:<math>W'(t) = P(t)</math> |
:<math>W'(t) = P(t)</math> |
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+ | :<math>\nabla \cdot V = \vec{E}</math> |
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+ | :f(x)=f'(X) |
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+ | : |
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==See also== |
==See also== |
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*[[Table of derivatives]] |
*[[Table of derivatives]] |
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*[[Integration]] |
*[[Integration]] |
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+ | *[[w:c:math:Derivative|Derivative]] on Math wiki |
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[[Category:Mathematical operations]] |
[[Category:Mathematical operations]] |
Latest revision as of 11:12, 17 September 2019
The derivative of a function is a second function showing the rate of change of the dependent variable compared to the independent variable. It can be thought of as a graph of the slope of the function from which it is derived. The process of finding a derivative is called differentiation. The derivative of y with respect to x (denoted as y') is equal to
The inverse of differentiation is integration.
Multivariable extensions[]
For multivariable scalar fields, either a gradient (a vector field representing the direction of greatest change) or directional derivative (a scalar representing the rate of change in a particular direction) can be taken. The two equivalents to derivation over a scalar field are divergence and curl.
Derivatives in physics[]
- f(x)=f'(X)
See also[]
- Table of derivatives
- Integration
- Derivative on Math wiki