Question

Find the derivative of y=sin^(2)(x)cos^(2)(x)

Answer 1

`sin^(2)x \ cos^(2) x= (1)/(2) (1-cos2x) * (1)/(2) (1+cos2x) \\ = (1)/(4) (1- cos^(2) 2x) \\ = (1)/(4) ( sin^(2) 2x +cos^(2) 2x- cos^(2) 2x) \\ = (1)/(4) ( sin^(2) 2x) \\ = (1)/(4) ( (1)/(2) (1-cos2(2x))) \\ = (1)/(8) (1-cos4x) \\ (d)/(dx) (sin^(2)x \ cos^(2) x)= (1)/(8) (d)/(dx) (1-cos4x) \\ = (1)/(8) [-4(-sin4x) \\ (1)/(2) sin4x`