Let $I\subset\R$ be an open interval.
Let $U$ be an open subset of $\R^n$.
Let $f: U \to \R$ be a real-valued function.
Then $f$ is continuously differentiable in the open set $U$ if and only if:
- $(1): \quad f$ is differentiable in $U$.
- $(2): \quad$ the partial derivatives of $f$ are continuous in $U$.
Let $U \subset \R^n$ be an open set.
Let $f: U \to \R^m$ be a vector-valued function.
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): continuously differentiable