Let, f(x) = x , if x is rational

= 0 , if x is irrational.

Then at x=0, which one of he followings is true?

(a) both f and $\displaystyle f^2$ are differentiable

(b) neither f nor $\displaystyle f^2$ are differentiable

(c) $\displaystyle f^2$ is continuous but not differentiable

(d) $\displaystyle f^2$ is differentiable but f is not

please help.