Category:Definitions/Partial Differentiation
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This category contains definitions related to Partial Differentiation.
Related results can be found in Category:Partial Differentiation.
The partial derivative of $f$ with respect to $x_i$ at $a$ is denoted and defined as:
- $\map {\dfrac {\partial f} {\partial x_i} } a := \map {g_i'} {a_i}$
where:
- $g_i$ is the real function defined as $\map g {x_i} = \map f {a_1, \ldots, x_i, \dots, a_n}$
- $\map {g_i'} {a_i}$ is the derivative of $g$ at $a_i$.
Subcategories
This category has the following 2 subcategories, out of 2 total.
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G
Pages in category "Definitions/Partial Differentiation"
The following 29 pages are in this category, out of 29 total.
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P
- Definition:Partial Derivative
- Definition:Partial Derivative of Real-Valued Function
- Definition:Partial Derivative of Real-Valued Function at Point
- Definition:Partial Derivative/Higher Derivative
- Definition:Partial Derivative/Higher Derivative/Fourth Derivative
- Definition:Partial Derivative/Higher Derivative/Third Derivative
- Definition:Partial Derivative/Notation
- Definition:Partial Derivative/Order
- Definition:Partial Derivative/Real Analysis
- Definition:Partial Derivative/Real Analysis/Open Set
- Definition:Partial Derivative/Real Analysis/Point
- Definition:Partial Derivative/Real Analysis/Point/Definition 1
- Definition:Partial Derivative/Real Analysis/Point/Definition 2
- Definition:Partial Derivative/Second Derivative
- Definition:Partial Derivative/Value at Point
- Definition:Partial Derivative/Vector Function
- Definition:Partial Derivative/Vector Function/Cartesian 3-Space
- Definition:Partial Differential Operator