Sometimes I see an exercise like this:
Let $f:[a,b] \to \mathbb R$ be differentiable. (A few more givens here.) Show that $f'$ has such-and-such property.
What is usually meant by that? Should $f'$ be defined on $[a,b]$ with one-sided derivatives in $a,b$? Or should one rather assume $(a,b)$ to be the domain of $f'$?