I have this kind of exercise:

Let $\displaystyle f \in F[X]$ be an irreducible polynomial where F has characteristic $\displaystyle p > 0 $. Express $\displaystyle f(X) = g(X^{p^m})$ where $\displaystyle m \in N $ is a large as possible. Show that g is irreducible and separable.

I know how to show that g is irreducible, but how I show that g is separable?