# 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:

- $\dfrac {\partial f}{\partial x_i}(a) := g_i'(a_i)$

where:

- $g_i$ is the real function defined as $g \left({x_i}\right) = f \left({a_1, \ldots, x_i, \dots, a_n}\right)$
- $g'(a_i)$ 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