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Definition

Given a calculus field?sequentially Cauchy complete Archimedean ordered field $\mathrm{<span><del\; class="diffmod">\; F</del><ins\; class="diffmod">\; ℝ</ins></span>}$ F \mathbb{R} of scalars, let $V$ be a $\mathrm{<span><del\; class="diffmod">\; F</del><ins\; class="diffmod">\; ℝ</ins></span>}$ F \mathbb{R}-calculus vector space?real vector space $V$, and let $f:V\to \mathrm{<span><del\; class="diffmod">\; F</del><ins\; class="diffmod">\; ℝ</ins></span>}$ f:V \to F \mathbb{R} be a directionally differentiable function valued in scalars. Given a vector $w:V$, the directional derivative $\Del_{w}$ is pointwise defined as

See also

• calculus field?sequentially Cauchy complete Archimedean ordered field

• calculus vector space?real vector space

• Newton-Leibniz operator

• partial derivative