1. Stating the problem: Find $\frac{dy}{dx}$ for the function given by $y^3 = 4x$. 2. Formula and rules: We will use implicit differentiation since $y$ is given implicitly by the equation $y^3 = 4x$. 3. Differentiate both sides with respect to $x$: $$\frac{d}{dx}(y^3) = \frac{d}{dx}(4x)$$ Using the chain rule on the left side: $$3y^2 \frac{dy}{dx} = 4$$ 4. Solve for $\frac{dy}{dx}$: $$\frac{dy}{dx} = \frac{4}{3y^2}$$ 5. Explanation: We treated $y$ as a function of $x$, so when differentiating $y^3$, we multiplied by $\frac{dy}{dx}$ due to the chain rule. The derivative of $4x$ is simply 4. Final answer: $$\frac{dy}{dx} = \frac{4}{3y^2}$$