continuity of $f ' $

Question

if $f$ is differentiable on $(a,b)$ can we say that $f'$ is continuous on $(a,b)$?

I tried some functions and it seems that we can say so but I'm not sure.

Answer 1

Try $$f(x)=\left\{\begin{array}{cc}x^2\sin(\frac{1}{x}),& x\neq 0\\ 0,& x=0\end{array}\right.$$