1. Problem: Find the derivative $\frac{dy}{dx}$ of $y = 5x^4$. 2. Formula: Use the power rule for derivatives, which states that if $y = ax^n$, then $\frac{dy}{dx} = a n x^{n-1}$. 3. Applying the power rule: $$\frac{dy}{dx} = 5 \times 4 x^{4-1} = 20x^3$$ 4. Explanation: We multiply the coefficient 5 by the exponent 4, then subtract 1 from the exponent to get the new power of $x$. 5. Final answer: $$\frac{dy}{dx} = 20x^3$$