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Definition

Given a sequentially Cauchy complete Archimedean ordered field $\mathbb{R}$ of scalars, let $V$ be a $\mathbb{R}$-real vector space $V$, and let $f:V \to \mathbb{R}$ be a directionally differentiable function valued in scalars. Given a vector $w:V$, the directional derivative $\Del_{w}$ is pointwise defined as

See also

• sequentially Cauchy complete Archimedean ordered field

• real vector space

• Newton-Leibniz operator

• partial derivative