Define $f:[0,1]\to [0,1]$ by
$$f(x)=\begin{cases}0, &x=0,\\ \\ \sum\limits_{r_n
where $\{r_n \}_{n\in \mathbb N} =\mathbb Q \cap (0,1) $.
How to show that the derivative $f'(x)=0$ a.e.?
I can show this function is increasing and discontinuous at every rational, and how to word on?