Okay, just to make sure I'm understanding:
x + y = 6
y = 6 - x
So if x = 2, 4, 5, that would make y = 4, 2, 1, and so on.
Hmm, okay. I don't really see it?
Using the product rule I got:
(2xy + x2) + (y2 + 2y) = 0
The parentheses might be wrong, and I might've taken the derivative of 6 too...