Question

F(x)=sin5x sin3x +cos5x cos3x как наити производную

Answer 1

F' = (sin'(5x)*sin(3x) + sin(5x)*sin'(3x)) + (cos'(5x)*cos(3x) + cos(5x)*cos'(3x)) = 5*cos(5x)*sin(3x) + 3cos(3x)*sin(5x) - 5sin(5x)*cos(3x) - 3sin(3x)*cos(5x) = 2sin(3x)*cos(5x) - 2sin(5x)*cos(3x) = 2*(sin(3x)*cos(5x) - sin(5x)*cos(3x)) = 2sin(3x-5x) = 2sin(-2x) = -2sin(2x)