Definition:Partial Derivative/Order

Definition
$u = \map f {x_1, x_2, \ldots, x_n}$ 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.