Product rule in terms of implicit differentiation

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?

Quote:

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Originally Posted by CFem

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.

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Isolate the dy/dx terms and solve for dy/dx