So I read a definition of separable polynomial like this:
"A separable polynomial is an irreducible polynomial which does not have multiple root in its splitting field."
So, it is equivalent that $f$ and $f'$ have common root, right? My question is, does it count if $f'= 0$, I mean in a field of characteristic $p>0$, $f'$ could be $0$ but $f$ only needs to be in $K(X^p)$, then how do we decide if $f$ is separable?