show that (d/dx)[(x)sin(x)+cos(x)]=(x)cos(x)

Question

(d/dx)[(x)sin(x)+cos(x)]=(x)cos(x).

Answer 1

d/dx[(x)sin(x)+Cos(x)]

= d/dx((x)Sin(x))+d/dx(cos(x))

Apply product rule d/dx(uv) = uv'+vu'

d/dx(Sin(x)) = Cos(x)

d/dx(Cos(x)) = -Sin(x)

= (x)Cos(x)+Sin(x)-Sin(x)

= (x)Cos(x)

d/dx[(x)sin(x)+Cos(x)] = (x)Cos(x)