I'm trying to find the first and second derivative (at 0) of a rather strange function. Let g(x) = 1 if x is rational, -1 if x is irrational. Let f(x) = x^3* g(x). I convinced myself earlier that the first and second derivative at 0 does not exist as the function is not continuous, but i'm not sure if i'm right. Is there a good way to do this using the definition of a derivative(I can't figure out how), any other help would be great too.