In mathematics, the **directional derivative** of a multivariate differentiable 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**. It therefore generalizes the notion of a partial derivative, in which the rate of change is taken along one of the coordinate curves, all other coordinates being constant.

The directional derivative is a special case of the GĂ˘teaux derivative.

Read more about Directional Derivative: Definition, In Differential Geometry, Normal Derivative, In The Continuum Mechanics of Solids

### Famous quotes containing the word derivative:

“When we say “science” we can either mean any manipulation of the inventive and organizing power of the human intellect: or we can mean such an extremely different thing as the religion of science the vulgarized *derivative* from this pure activity manipulated by a sort of priestcraft into a great religious and political weapon.”

—Wyndham Lewis (1882–1957)