# Definition:Continuously Differentiable/Real Function

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## Definition

### On an Open Interval

Let $I\subset\R$ be an open interval.

Then $f$ is **continuously differentiable on $I$** if and only if $f$ is differentiable on $I$ and its derivative is continuous on $I$.

### On an Open Set

Let $I \subset \R$ be an open set.

Then $f$ is **continuously differentiable on $I$** if and only if $f$ is differentiable on $I$ and its derivative is continuous on $I$.