Definition:Differentiable Mapping/Vector-Valued Function/Point/Definition 2

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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.


$f$ is differentiable at $x \in \R^n$ if and only if for each real-valued function $f_j: j = 1, 2, \ldots, m$:

$f_j: \mathbb X \to \R$ is differentiable at $x$.