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 $a_i$.