# Definition:Continuously Differentiable/Real Function

## 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 $I$.