Let (y = cos^2x)

Then, (y = (cos x)^2)

Using the chain rule,

(dy/dx = 2(cos x)(-sin x))

(dy/dx = -2(cos x)(sin x))

Therefore, the derivative of (cos^2x) is (-2(cos x)(sin x)).

Let (y = cos^2x)

Then, (y = (cos x)^2)

Using the chain rule,

(dy/dx = 2(cos x)(-sin x))

(dy/dx = -2(cos x)(sin x))

Therefore, the derivative of (cos^2x) is (-2(cos x)(sin x)).