1) x^2 + xy - y^2 = 4

x^2 + x*y(x) - y(x)^2 = 4

I understand this much: 2x + ____ + 2y*(dy/dx) = 0

But I don't understand how to differentiate the middle portion properly. I'm assuming it's just the product rule, but doing it didn't lead me to the right answer.

2) x^4(x + y) = y^2(3x - y)

Product rule again?