CAS and exponents issues

[Albert Chan]

(10-03-2018 08:34 AM)sasa Wrote:  It would be definitely nice touch for simplification and factorization on last step.

Your non-simplified diff(...) result actually look pretty good to me.
It clearly shown what is done to the expression (product rule).

diff(((1+x^2)/2)*tan(x),x) => (2*x/2)*tan(x)+((1+x^2)/2)*(1+tan(x)^2)

If factorization or simplification (whatever that meant) were needed, do it in separate step.
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About what is simplified form, it is very subjective.

Is 2^10 simpler than 1024 ? How about 2^20 vs 1048576 ?

Is 6^(1/3) really simpler than factorized 2^(1/3)*3^(1/3) ?
If true, why is 9^(1/5) not simpler than 3^(2/5) ?

Assuming 3 "simpler" than 9, 1/5 "simpler" than 2/5, who win the simpler race ?