Differentiate y = (sin(x))^2 (find dy/dx)
This a relatively simple question which requires the use of the chain rule to solve. First we set u = sin(x) so we then have y = u2 . Next we perform do differentiations, one on u as a function of x and the other on y as a function of u: dy/du = 2u du/dx = cos(x) Next we note that dy/dx = (dy/du)(du/dx) note how the du terms cancel out, striclty speaking it doesn't quite work this way but for this level it's fine to think of it as such. So dy/dx = 2ucos(x). We finally substitue sin(x) in for u and we have dy/dx = 2*sin(x)*cos(x).
