# Category:Examples of Partial Derivatives

The partial derivative of $f$ with respect to $x_i$ at $a$ is denoted and defined as:
$\map {\dfrac {\partial f} {\partial x_i} } a := \map {g_i'} {a_i}$
$g_i$ 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 $a_i$.