Finding dy/dx by implicit differentiation

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Find dy/dx by implicit differentiation

x^2-4xy+y^2=4

I know to take the derivatives of both sides, which would be:

d/dx[x^2-4xy+y^2]=0

I'm not sure if I did it right, but I then got:

2x-4*(xdy/dx)+y+2y(dy/dx)=0

I don't know where to go from here, or even if the previous step is correct. Please help!

Edit: I have followed the advice given and I ended up with:

(x-2y)/(2x-1)

However this was incorrect. Someone please tell me what I am missing here.

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You are close! You forgot a coefficient on the $y$ term. You should have $$ 2x-4y-4x\frac{dy}{dx}+2y\frac{dy}{dx}=0 $$ Now you can solve for $\frac{dy}{dx}$ like any other variable.