 # Find (dy)/(dx) by implicit differentiation. x^2−4xy+y^2=4 batejavizb 2022-09-14 Answered
Find dydx by implicit differentiation.
x2−4xy+y2=4

My solution:
$\frac{d}{dx}{x}^{2}-\frac{d}{dx}4xy+\frac{d}{dx}{y}^{2}=\frac{d}{dx}4$
$2x-\left(4x{\right)}^{\prime }\left(y\right)+\left(4x\right)\left(y{\right)}^{\prime }+2y\frac{dy}{dx}=0$
$2x-4y\frac{dy}{dx}+4x\frac{dy}{dx}+2y\frac{dy}{dx}=0$
$\frac{dy}{dx}\left(-4y+4x+2y\right)=-2x$
$\frac{dy}{dx}=\frac{-2x}{4x-2y}$
$\frac{dy}{dx}=\frac{2y-x}{y-2x}$
I would like to understand why my answer is incorrect. If someone could take a look at my steps and explain to me where I went wrong it would be greatly appreciated!
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The third line should be
$2x-4y-4x\frac{dy}{dx}+2y\frac{dy}{dx}=0$
not
$2x-4y\frac{dy}{dx}+4x\frac{dy}{dx}+2y\frac{dy}{dx}=0$
and that plus sign error was also in the second line.

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