Differentiability Class

Definition

Differentiability class is a measure of the highest order of derivative that exists and is continuous for a function.

The function $f$ is called a $C^k$ function if the derivatives $f^{\prime },f^{\prime \prime },\dots ,f^{(k)}$ exist and continuous on its domain. $f\in C^k$ where $k\in {\mathbb{R}}_0^{+}$

As a special case, a $C^0$ function is a Continuous Function.