# Definition:Partial Derivative/Order

< Definition:Partial Derivative(Redirected from Definition:Order of Partial Derivative)

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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.