# Definition:Continuously Differentiable/Vector-Valued Function/Open Set

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## Definition

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 $U$** if and only if $f$ is differentiable in $U$ and its partial derivatives are continuous in $U$.