Definition:Partial Derivative/Order
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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.