Ah! Why doesn't it work!? Examples are a good way to see and learn, I suppose. Can someone implicitly differentiate, oh, for example:

y^2=(x^2-9)/(x^2+9)

? I have:

2y(dy/dx)=2x/(2x)
2y(dy/dx)=1
dy/dx=1/(2y)

But my book doesn't agree with me. Wah!