Definition:Differentiable Mapping/Vector-Valued Function/Point

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.

Then $f$ is differentiable at $x \in \R^n$ if, for each real-valued function $f_j: j = 1, 2, \ldots, m$:
 * $f_j: \mathbb X \to \R$ is differentiable at $x$