\begin{definition}[Definition:Differentiability Class/Domain Restriction]
Let $f: \R \to \R$ be a real function.
Let $S \subseteq \R$ be a subset of $\R$ on which the $n$th derivative of $f$ is continuous on $S$.
Then $\map f x$ is of '''differentiability class''' $C^n$ on $S$.
\end{definition}