Question

sin 3x cos 5x differntiate it

Answer 1

Hey there,

let sin 3x=u,cos 5x=v,

=>d(sin 3x cos 5x)/dX=d(uv)/dx

=>d(uv)/dx=u (v)'+v (u)'

=sin 3x (cos 5x)'+cos 5x ( sin 3x)'

=sin 3x d/dx(cos 5x)+cos 5x d/dx(sin
3x)

=sin 3x [d/d5x (cos 5x)×d/dx(5x)]+

cos 5x[d/d3x (sin 3x)×d/dx(3x)]

=sin 3x (-sin5x)×5+cos 5x(cos 3x)×3

=-5 sin 3x sin 5x+3 cos 3x cos 5x.

Hope it helps