if [tex]y=1/[x+y)[/tex] then [tex]y^{2}+xy=1[/tex]. Differentiate to obtain:
[tex]
2y\frac{dy}{dx}+y+x\frac{dy}{dx}=0
[/tex]
Re-arrange to obtain dy/dx
hunt_mat is correct. Rearranging is much quicker, but taking the quadratic route is very useful to check your answer.
Edit: If I let v = x + y, then y = 1/v and dy/dx = -1/v^2 dv/dx. However, continuing this does not give me the right answer; why not? EDIT: Nevermind, I figured it out. :)