simplifly calculus derivitives?

Question

I pretty much have the derivitives down, its just when I get to the cleaning up I have trouble. can someone show me how to clean these two up? Ill also give you the original problem.

1. f(x)= [x^4 + (1/x) ]^5
f'(x)= 5(x^4 + (1/x))^4 * (4x^3 + (-1/x^2))


2. f(x) = sin (cube root of x) + (cube root of sin x)
::Hope I wrote that ok::
f'(x) = cos (x)^(1/3) * (1/3)x^(-2/3) + (1/3)(sin x)^(-3/3) * cos x

im not too sure if that ones right or not... now that i look at it.. lol... I know that you cant have negative exponents, so some of that stuff means its in the denominator and is a square root or cube root or whatever too...

Answer 1

f'(x) = cos (x)^(1/3) * (1/3)x^(-2/3)
...looks right
+ (1/3)(sin x)^(-3/3) * cos x ...Nope!

+ (cos x)^(1/3) * (1/3)(sin x)^(-2/3)
...looks better to me