# Directional derivative

In mathematics, the **directional derivative** of a multivariate differentiable (scalar) function along a given vector **v** at a given point **x** intuitively represents the instantaneous rate of change of the function, moving through **x** with a velocity specified by **v**.

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The directional derivative of a scalar function *f* with respect to a vector **v** at a point (e.g., position) **x** may be denoted by any of the following:

- .

It therefore generalizes the notion of a partial derivative, in which the rate of change is taken along one of the curvilinear coordinate curves, all other coordinates being constant. The directional derivative is a special case of the Gateaux derivative.