Definition:Differentiable Mapping/Vector-Valued Function/Region

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Definition

Let $\mathbb X$ be an open subset of $\R^n$.

Let $f = \left({f_1, f_2, \ldots, f_m}\right)^\intercal: \mathbb X \to \R^m$ be a vector valued function.

Let $S \subseteq \mathbb X$.


Then $f$ is differentiable in the open set $S$ if and only if $f$ is differentiable at each $x$ in $S$.


This can be denoted $f \in \mathcal C^1 \left({S, \R^m}\right)$.


Also see


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