y=4(x+1)^3sin^2(6x^2 -2)
I know how to do the first part, I just don't know how to differentiate sin^2(6x^2-2)
I would think of it more like $\displaystyle (\sin{(6x^2-2)})^2$ to see how the chain rule is used multiple times. In the most general sense, you have something squared, just like [f(x)]^2. So start with the power rule and you get 2*[f(x)]*[f'(x)].
So it would be like $\displaystyle 2(\sin{(6x^2-2)})^{1}*\left( \frac{d}{dx}[\sin{6x-2}] \right)$