how do I differentiate this function implicitly

Question

How do I differentiate $$\frac{(x^2 - 4y^2)} {(x^2 + xy^2)} = 2$$ implicitly? I did it by bringing the denominator over to the other side, and I got $$\frac{-(2x + 2y^2)}{(4xy + 8y)}$$

---

Here are the images of the question and the suggested answer.

Answer 1

Ok, here's how you'd do it: We have $$\frac{x^2-4y^2}{x^2+xy^2}=2$$ So$$x^2-4y^2=2x^2+2xy^2$$ Differentiating implicitly: $$2x-8y\frac{dy}{dx}=4x+(2y^2+4xy\frac{dy}{dx})$$(using product rule as well) so $$4xy\frac{dy}{dx}+8y\frac{dy}{dx}=-2x-2y^2$$ so$$\frac{dy}{dx}(4xy+8y)=-2x-2y^2$$ and finally $$\frac{dy}{dx}=\frac{-2x-2y^2}{4xy+8y}$$ I hope that helped!