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- 1)Find the anti derivative for sin(x^2) 2x(a) From sin2 x + cos2 x = 1, we have f(x) + g(x) = 1. Take the derivative of both sides of this equation to obtain f' (x) + g' (x) = 0. This implies f'(x) = -g'(x). (b) f' (x) = 2 sin x cos x, and g'(x) = 2(cosx)(-sinx) = -2sin x cos x. So, f'(x) = -g'(x).Find the derivative of f ( x ) = 6 sin ^2 ( x ) + 6 cos^2 ( x ) at x = -6.5