[tex]f(x) = \cos^2 x \\\\f'(x) = 2 \cos x ( - \sin x) = - 2 \cos x \sin x = -\sin 2x\\\\f''(x) = -2\cos 2x\\\\\text{The second derivative of}~ \cos^2 x ~ \text{is}~ -2 \cos 2 x[/tex]
