# Definition:Piecewise Continuously Differentiable Function/Definition 2

## Definition

Let $f$ be a real function defined on a closed interval $\left[{a \,.\,.\, b}\right]$.

$f$ is **piecewise continuously differentiable** if and only if:

- there exists a finite subdivision $\left\{{x_0, \ldots, x_n}\right\}$ of $\left[{a \,.\,.\, b}\right]$, $x_0 = a$ and $x_n = b$, such that:
- $f$ is continuously differentiable on $\left[{x_{i−1} \,.\,.\, x_i}\right]$, the derivative at $x_{i−1}$ understood as right-handed and the derivative at $x_i$ understood as left-handed, for every $i \in \left\{{1, \ldots, n}\right\}$.

## Also see

## Sources

- 1991: Reinhold Remmert:
*Theory of Complex Functions*(2nd ed.): Part $\text{B}$, Ch. $6$: $\S 1.1$