It's fine.
I get .
Let . Then, .
Substitute in f(x).
.
Then, f'(x) is easy to compute.
Substitute in f'(x).
Get rid of the double negatives.
Next, get rid of the sines and cosines: and .
Get rid of double negatives.
Get rid of the fraction within a fraction within a fraction within a fraction.
Edit: Prove It's method seems less convoluted. :P