# Thread: Product rule in terms of implicit differentiation

1. ## 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?

2. 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.
$\displaystyle u = x \: \rightarrow \: u' = 1$

$\displaystyle v = y \: \rightarrow \: v' = \frac{dy}{dx}$

$\displaystyle \frac{dy}{dx} = u'v + v'u = y + x\frac{dy}{dx}$

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