Polynomial derivative causes Prime to Crash?

[parisse]

roadrunner: nothing is wrong. You get the result as rootof(P,Q) i.e. P(alpha) where Q(alpha)=0. This is because the simplifier rewrite all algebraic extensions in a unique one, in order to certify that it will not miss a simplification, the analog as when you add fractions like 1/2+1/3+1/6 you can get a simplification to an integer. However here it requires heavy computations.
I would recommend not to run simplify on expressions with fractional powers, by the way the title of the topic is misleading, this is not a polynomial derivative.

Regarding fractional powers, the CAS rewrites them as polynomials over simpler intermediate variables, here x^(3/5) as x^(1/5)^3.