Let $f:\mathbb{R} \rightarrow \mathbb{R}$. Is it possible that $f$ has a derivative that nowhere continuous on its domain? Please provide an example if possible.
Thanks
Let $f:\mathbb{R} \rightarrow \mathbb{R}$. Is it possible that $f$ has a derivative that nowhere continuous on its domain? Please provide an example if possible. Thanks 


I would say "no". $f$ is continuous, and that derivative is therefore of first Baire class. Such a function is continuous except on a set of first category. Now I'll investigate Pietro's reference and see where (or if) I went wrong. (checked) In fact, Pompeiu's derivative is continuous on a dense $G_\delta$ set (where it vanishes) after all. 

