Definition:Differentiable Mapping/Real Function/Interval

Definition
Let $f$ be a real function defined on an open interval $\left({a \,.\,.\, b}\right)$.

Let $f$ be differentiable at each point of $\left({a \,.\,.\, b}\right)$.

Then $f$ is differentiable on $\left({a \,.\,.\, b}\right)$.