\begin{definition}[Definition:Partial Derivative/Order]
$u = \map f {x_1, x_2, \ldots, x_n}$ be a function of the $n$ independent variables $x_1, x_2, \ldots, x_n$.
The '''order''' of a partial derivative of $u$ is the '''number of times it has been (partially) differentiated''' by at least one of $x_1, x_2, \ldots, x_n$.
For example:
:a second partial derivative of $u$ is of '''second order''', or '''order $2$'''
:a third partial derivative of $u$ is of '''third order''', or '''order $3$'''
and so on.
Category:Definitions/Partial Differentiation
\end{definition}