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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

See also

• calculus field?

• calculus vector space?

• Newton-Leibniz operator

• partial derivative