directional derivative

English

directional derivative (plural directional derivatives)

(calculus) A function which measures the rate of change of some other function at any point in a particular direction; formally, the directional derivative of a scalar function $f(\mathbf {x} )=f(x_{1},x_{2},\ldots ,x_{n})$ along a vector $\mathbf {v} =(v_{1},\ldots ,v_{n})$ is the function $\nabla _{\mathbf {v} }{f}$ defined by the limit $\nabla _{\mathbf {v} }{f}(\mathbf {x} )=\lim _{h\to 0}{\frac {f(\mathbf {x} +h\mathbf {v} )-f(\mathbf {x} )}{h}}$ .