Using the usual definition of inseparable and separable degrees (from Abstract Algebra by Dummit and Foote) I proved the following:
If $f$ is a irreducible polynomial. The separable degree of $f$ is the number of distinct roots of $f$ in a splitting field, the inseparable degree of $f$ is the multiplicity of each root.
The book does not mention this result, but I think it is true. Is it true?
This answer is just for remove my question from unanswered section.