Chapter 2 - Differentiation - 2.5 Exercises - Page 145: 1

$\dfrac{dy}{dx}=-\dfrac{x}{y}.$

Using Implicit Differentiation: $\dfrac{d}{dx}(x^2)+\dfrac{d}{dx}(y^2)=\dfrac{d}{dx}(9)\rightarrow$ $2x+\dfrac{dy}{dx}(2y)=0\rightarrow$ $\dfrac{dy}{dx}(-2y)=2x\rightarrow$ $\dfrac{dy}{dx}=-\dfrac{x}{y}.$