it looks easy but, I do not know what I did wrong:
what is the derivative of f(x) = cosx -1/3(cos^3 x )
the answer is -sin^3 x
while I got -sinx+cos^2 x * sinx !

and also with this :
f(x) = 1/ (x+ sqr(x^2 +1))

Your solution is correct. Only in another form.

-sin^{3}(x)=-sin(x)+cos^{2}(x)sin(x)

My word! Have you never heard of trigonometric identities? Here's a link so you never run into that problem again. http://www.clarku.edu/~djoyce/trig/identities.html