## Question about separability

I have this kind of exercise:

Let $f \in F[X]$ be an irreducible polynomial where F has characteristic $p > 0$. Express $f(X) = g(X^{p^m})$ where $m \in N$ 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?