What is the derivative of cos^2x?

Let y = cos²x
Differentiating on both sides, w.r.t x, we get;
dy/dx = d/dx (cos²x)
= (d/dx) (cos x)²
= 2 cos x (d/dx) cos x
= 2 cos x (-sin x)
= -2 sin x cos x
= – sin 2x
Therefore, the derivative of cos square x is -sin 2x.