Hi,

I'm having some trouble with this problem, I'm supposed to find the derivative:

$\displaystyle y = \sin^2(\cos(3x^{-2}))$

I know that the Chain Rule can be applied, but to what extent? There are three terms. I tried to simplify it to

$\displaystyle 2\cos(\cos(3x^{-2}) \cdot -\sin(3x^{-2})$

Would the next step be to differentiate the right side? Also, on the left side, you could differentiate again and again only to still have the $\displaystyle \cos(3x^{-2})$ - how do you know for certain that once is enough?

Thanks in advance!