Найдите производную.

cos2xsinx+sin2xcosx

F (x) = cos (2x) sinx+sin (2x) cos (x)

Формула: f (x) = uv, f' (x) = u'v+uv'

cos (2x) '=-2sin (2x)

sin (x) '=cos (x)

sin (2x) '=2cos (2x)

cos (x) '=-sin (x)

f' (x) = (-2sin (2x) sin (x) + cos (2x) cos (x)) + (2cos (2x) cos (x) + sin (2x) (-sin (x)) =

=-2sin (2x) sin (x) + cos (2x) cos (x) + 2cos (2x) cos (x) - sin (2x) sin (x) =

=-3sin (2x) sin (x) + 3cos (2x) cos (x)