Differentiate y=(sin(x))^(2)

Using the chain rule of dy/dx=dy/du * du/dx we label sin(x) as u. Now we differentiate u with respect to x, getting cos(x). Then we differentiate u² , getting 2u. Mutiplying these together gets us 2u*cos(x). Clearly we don't want u anymore, so replace u with sin(x) and obtain 2sin(x)cos(x) as the final answer!