I was wondering whether there is a standard notation for the set of differentiable functions (but the derivative doesn't not need to be bounded, i.e. not necessarily $C^1$)
This question is in the context of the mean value theorem:
f $\in C[a, b]$ and differentiable on (a, b) $\implies$ $\exists c \in (a, b)$ s.t. $f'(c) = \frac{f(b) - f(a)}{b - a}$
Many thanks in advance!