試求以下函數的導數dy/dx

The answer should be as simplified as possible as follows:

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d(sin 2x)/dx
=[d(sin 2x)/d(2x)][d(2x)/dx]
=2 cos 2x
d(cos^2 x)/dx
=[d(cos^2 x)/d(cos x)][d(cos x)/dx]
=2 cos x (-sin x)
=-2 sin x cos x
dy/dx=sin 2x d(cos^2 x)/dx+cos^2 x d(sin 2x)/dx
=(-2 sin x cos x) sin 2x+cos^2 x (2 cos 2x)
=-2 sin x sin 2x cos x+2 cos^2 x cos 2x