# 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 $a_i$.

## Pages in category "Definitions/Partial Differentiation"

The following 15 pages are in this category, out of 15 total.

### P

- Definition:Partial Derivative
- Definition:Partial Derivative of Real-Valued Function at Point
- Definition:Partial Derivative/Notation
- 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 Differential Operator