directional derivative

directional derivative (plural directional derivatives)

1. (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 ${\displaystyle f(\mathbf {x} )=f(x_{1},x_{2},\ldots ,x_{n})}$ along a vector ${\displaystyle \mathbf {v} =(v_{1},\ldots ,v_{n})}$ is the function ${\displaystyle \nabla _{\mathbf {v} }{f}}$ defined by the limit ${\displaystyle \nabla _{\mathbf {v} }{f}(\mathbf {x} )=\lim _{h\to 0}{\frac {f(\mathbf {x} +h\mathbf {v} )-f(\mathbf {x} )}{h}}}$.

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