Solving a derivative through implicit differentiation 
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?

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.
