\begin{definition}[Definition:Differentiable Mapping/Vector-Valued Function/Point/Definition 2]
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 $x \in \R^n$ {{iff}} for each real-valued function $f_j: j = 1, 2, \ldots, m$:
:$f_j: \mathbb X \to \R$ is differentiable at $x$.
Category:Definitions/Differentiable Vector-Valued Functions
\end{definition}