Let (V,\| \|) and (W,\| \|) be finitely dimensional normed vector spaces, G\subseteq V an open subset, and f\colon G\rightarrow W a function. Furthermore, let x\in G be a point and v\in V a fixed vector. Then we call the directional derivative of f along v, if the limit. \operatorname {lim} _{\substack{t\rightarrow 0,\\t\neq 0}}\,{\frac {f(x+tv)-f(x)}{t}}
exists. We also denote the directional derivative as
\left(D_{v}f\right)\left(x\right),
(read "directional derivative of f along the vector v at the point x").
Definitions: 1
