Definition:Differentiable Mapping/Vector-Valued Function/Point/Definition 3
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Definition
Let $\mathbb X$ be an open subset of $\R^n$.
Let $f = \tuple {f_1, f_2, \ldots, f_m}^\intercal: \mathbb X \to \R^m$ 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 $x$.