Use the product rule to differentiate y=2xsinx

The product rule states that y=uv and dy/dx=(u)dv/dx + (v)du/dx. As the equation is in this form we can let u=2x and v=sinx. Therefore du/dx=2 and dv/dx=cosx. Substituting for u and v we get dy/dx=(2x)(cosx) + (sinx)(2) so dy/dx=2(xcosx + sinx).