when tcollect goes (sorta) buggy....

[quinyu]

In differentiating the expression

(x^2)*sin(x)^4+x*(cos(x))^(-2)

the first response is essentially equivalent to the answer known to be the shortest to me:

4(x^2)*sin(x)^3*cos(x)+2x*sin(x)^4+2x*sin(x)*cos(x)^(-3)+cos(x)^(-2). The HP Prime result has a fraction, with denominator being cos(x)^3, as to prevent the negative powers of trigonometric functions in the numerator.

But then, on using tcollect(Ans) (which usually helps tidying trigonometric expressions), the result gets much worse, sprinkled with square roots, absolute values, sign functions etc. When asked to simplify, the calculator just gets stuck (I gave it 15 minutes and couldn't finish.) Either way, when tcollect cannot make an expression tidier, it should just return the original... or at least, provide an option for it to influence this behavior.