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 $a_i$.