1. **Problem:** Find the derivative of $$y = \frac{x^3}{3} + \frac{x^2}{2} + \frac{x}{4}$$ 2. **Formula:** Use the power rule $$\frac{d}{dx} x^n = n x^{n-1}$$ and constant multiple rule. 3. **Work:** $$y' = \frac{d}{dx} \left( \frac{x^3}{3} \right) + \frac{d}{dx} \left( \frac{x^2}{2} \right) + \frac{d}{dx} \left( \frac{x}{4} \right)$$ $$= \frac{1}{3} \cdot 3x^{3-1} + \frac{1}{2} \cdot 2x^{2-1} + \frac{1}{4} \cdot 1x^{1-1}$$ $$= x^2 + x + \frac{1}{4}$$ 4. **Explanation:** We applied the power rule to each term, multiplied by constants, and simplified. **Final answer:** $$y' = x^2 + x + \frac{1}{4}$$