#Contents# * table of contents {:toc} ## Definition ## Given a [[calculus field]] $F$ of scalars and a type of indices $I$, one could define a [[calculus vector space]] $V \coloneqq F^I$ with canonical function $e:I \hookrightarrow V$. Let $f:V \to F$ be a [[directionally differentiable function]] valued in scalars, and given a vector $w:V$, the __directional derivative__ $\Del_{w}$ is pointwise defined as $$\Del_{w}(f)(v) \coloneqq \lim_{(x, y) \to (x, x)} \frac{f(v + x w) - f(v + y w)}{x - y}$$ ## See also ## * [[calculus field]] * [[calculus vector space]] * [[Newton-Leibniz operator]] * [[partial derivative]]