I am having trouble solving these problems, and finding the derivatives. I do not need them solved, but just explain the next step (unless otherwise noted):

1) sin(2x)*cos(2x)

' = sin(2x)(-2sin2x)+cos2x(2cos(2x))

- where did the two come from? wouldn't it just be cos(2x)?

2) cot(x)/sin(x) = cos(x)/sin^2(x)

- shouldn't there be a (-) since in the identity, there is one?

3) 4sec^2(x)

- Alright, this one, I do not quite understand what they did. It looks like they took the derivative of the number (they get 8) times the sec, then times the derivative of sec^2.