1. **Problem:** Find \( \frac{dy}{dx} \) using implicit differentiation for the equation \( x^2 + y^2 = 16 \). 2. **Formula and rules:** When differentiating implicitly, treat \( y \) as a function of \( x \), so use the chain rule: \( \frac{d}{dx}[y^2] = 2y \frac{dy}{dx} \). 3. **Differentiate both sides:** $$\frac{d}{dx}[x^2] + \frac{d}{dx}[y^2] = \frac{d}{dx}[16]$$ $$2x + 2y \frac{dy}{dx} = 0$$ 4. **Solve for \( \frac{dy}{dx} \):** $$2y \frac{dy}{dx} = -2x$$ $$\frac{dy}{dx} = \frac{-2x}{2y} = \frac{-x}{y}$$ **Answer:** \( \frac{dy}{dx} = \frac{-x}{y} \)