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2 sin² x = 1 - cos 2x
sin² x = 1/2 - 1/2 cos 2x
f(x)= sin² x -cos 2x
f(x) = 1/2 - 1/2 cos 2x - cos 2x
f(x) = 1/2 - 3/2 cos 2x
f'(x) = 0 - 3/2 (-2 sin 2x)
f '(x) = 3 sin 2x