CAS and exponents issues

[parisse]

I agree that it would be nice to have some rewriting command to collect exponents 2^(1/3)*3^(1/3) as 6^(1/3) but this is not a simplification failure : as I said simplify will correctly detect that 2^(1/3)*3^(1/3)-6^(1/3) is 0 and that is what is important.

As for diff(acos(x),x,6), there is intermediate rewrite between each derivative, otherwise diff(acos(x),x,30) would run forever, but there is no factorization, I don't think it accelerates computations for generic expressions (factorization may be costly, much more than rewriting an expression as an irreductible fraction).

You are of course free to think differently, but implementing is much harder than speaking, that's why I was curious to see what your CAS was really capable to do.