Can you help with one more?
X^2+2xy+y^2=15
2x+2x(dy/dx)+2y+2y(dy/dx)=0
Alright... I'm not convinced I've got this right as I'm quite new to implicit differentiation myself... but here's what I got step by step (do not take this as correct though).
$\displaystyle \frac{d}{dx}(x^2) + \frac{d}{dx}(2xy) + \frac{d}{dx}(y^2) = \frac{d}{dx}(15)$
$\displaystyle 2x + 2y + 2x + \frac{dy}{dx}\frac{d}{dy}(y^2) = 0$
$\displaystyle 2x + 2y + 2x + \frac{dy}{dx}2y = 0$
$\displaystyle \frac{dy}{dx} = \frac{4x + 2y}{2y} = \frac{2x + y}{y}$
like I said, check it first, I'm havent convinced myself...