# Requires Uploaded Supporting Analysis Find \frac{dy}{dx} by implicit differentiation. y^2-2x=4y

Requires Uploaded Supporting Analysis Find $\frac{dy}{dx}$ by implicit differentiation. ${y}^{2}-2x=4y$
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Arnold Odonnell

Given:${y}^{2}-2x=4y$
Differentiating with respect to x
$\frac{d}{dx}\left({y}^{2}-2x\right)=\frac{d}{dx}\left(4y\right)$

$\frac{d}{dx}\left({y}^{2}\right)-\frac{d}{dx}\left(2x\right)=4\frac{dy}{dx}$

$2y\frac{dy}{dx}-2=4\frac{dy}{dx}$

$\frac{dy}{dx}\left(2y-4\right)=2$

$\frac{dy}{dx}=\frac{2}{2y-4}$

$\frac{dy}{dx}=\frac{1}{y-2}$