simple one

px^{p-1}y^{q}+x^{p}qy^{q-1}\frac{dy}{dx}=(p+q)(x+y)^{p+q-1}(1+\frac{dy}{dx})

now i think u can rearrange the terms to get \frac{dy}{dx}

don't you think it would be tedious to do that and then cancelling the terms ....i think taking log first and then differentiating will help...

oops sorry
nishant sir has already given this method in "simple"

just take log and do naa.........u'll get..........

plogx*qlogy=(p+q)log(x+y)

u'll get remaning by differentiating.........