(cos2x sinx + sin2xcosx)' найдите производную

Question

(cos2x sinx + sin2xcosx)'

найдите производную

Answer 1

(cos2x sinx + sin2xcosx)'  = (cos2x sinx) ' +(sin2xcosx)' = -2sin2x*sinx + cosx*cos2x + 2cos2x*cosx - sinx*sin2x = -3sin2x*sinx+3cos2x*cosx = 3(cos2x*cosx - sin2x*sinx)=3cos3x