1. Problem: Find the derivative $\frac{dy}{dx}$ of $y = 5x^4$. 2. Formula: Use the power rule for derivatives, which states: $$\frac{d}{dx} x^n = n x^{n-1}$$ 3. Apply the power rule: $$\frac{dy}{dx} = 5 \times \frac{d}{dx} x^4 = 5 \times 4 x^{4-1} = 20 x^3$$ 4. Explanation: The power rule tells us to multiply by the exponent and then subtract one from the exponent. 5. Final answer: $$\frac{dy}{dx} = 20 x^3$$