The following statement was left as exercise in my Field Theory class.

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> Consider a field K and f $\in K[x] $ an irreducible polynomial. Prove that f is separable in some splitting field of f over K if every root of K is simple root which is equivalent to saying that derivative of f is non-zero.
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I am not able to understand how the definition of separability of a polynomial which is the fact that f is called a separable polynomial over K if all the roots of f are distinct in algebraic closure of K relates to saying that derivative of f is non -zero?

and hence I was unable to make any progress.