## Calculus, 10th Edition (Anton)

$\frac{dy}{dx}=-\frac{x}{y}$
Take the derivative of the whole argument in respect to $x$, giving $2x+2y\frac{dy}{dx}=0.$ Subtract 2x from each side and divide by $2y$ to get $\frac{dy}{dx}=-\frac{x}{y}$.