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 $I$.


Also see