# 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 $x_1, x_2, \ldots, x_n$.
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 $3$