Let $U \subset \mathbb R^n$ be open. Let $v \in \mathbb R^n$. The directional derivative of a function $f:U\to\mathbb R^m$ in the direction of $v$ at a point $a \in U$ is \(D_vf(a) = \frac{\partial f}{\partial v}(a) = \lim_{h\to 0}\frac{f(a+hv)-f(a)}{h}\) if this limit exists.
Wikidata ID: Q383851