Question

Найдите производную.
cos2xsinx+sin2xcosx

Answer 1

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)