continuity - derivative of differentiable function

Edited:

It is known that if $f$ is differentiable then the derivative function of $f$ is not always continuous. For instance $f(x)=x^2\sin (\frac{1}{x})$ for $x\neq 0$ and $f(0)=0$ if $x=0$. Then $f^{\prime}$ is discontinue at $x=0$.

Is there any differentiable function $f$ whose the derivative of $f$ has countable points of discontinuity?