Solving a derivative through implicit differentiation

Question

Find the derivative of $x^2+4xy+y^2=13$

So here is what I did: $$2x+4\left(x\frac{dy}{dx}+y\right)+2y\frac{dy}{dx}=0$$ $$4x\frac{dy}{dx}+2y\frac{dy}{dx}=-2x-4y$$ $$\frac{dy}{dx}(4x+2y)=-2x-4y$$ $$\frac{dy}{dx}=\frac{-2x-4y}{4x+2y}$$ But this isn't the correct answer.

Any help?

Answer 1

Given $$ x^2+4xy+y^2=13 $$ and apply the derivative operator $$ d(x^2+4xy+y^2)=d(13)\implies 2x+4x\frac{dy}{dx}+4y+2y\frac{dy}{dx}=0 $$ and so $$ \frac{dy}{dx}=-\frac{2x+4y}{4x+2y}=-\frac{x+2y}{2x+y} $$ and it appears you just didn't cancel the common factor 2 of the denominator and numerator.