\begin{definition}[Definition:Continuously Differentiable/Vector-Valued Function/Open Set]
Let $U \subset \R^n$ be an open set.
Let $f: U \to \R^m$ be a vector-valued function.
Then $f$ is '''continuously differentiable in $U$''' {{iff}} $f$ is differentiable in $U$ and its partial derivatives are continuous in $U$.
Category:Definitions/Differentiable Vector-Valued Functions
\end{definition}