The basic idea is to use the product and the chain rule. We have as follows:
d/dx [xy] = dx/dx*y + x*dy/dx = d/dx (1) = 0 by the product rule d/dx [uv] = du/dx*v + u*dv/dx. This gives us
y + x*dy/dx = 0.
Remember the chain rule that d/dx u(v(x)) = dv/dx * du(v(x))/dx.