1. **Problem:** Find the derivative of $$y = x^4 + 2x^3 + x^2$$. 2. **Formula:** The derivative of $$x^n$$ is $$\frac{d}{dx} x^n = nx^{n-1}$$. 3. **Step-by-step solution:** - Derivative of $$x^4$$ is $$4x^3$$. - Derivative of $$2x^3$$ is $$2 \times 3x^2 = 6x^2$$. - Derivative of $$x^2$$ is $$2x$$. 4. **Combine all:** $$\frac{dy}{dx} = 4x^3 + 6x^2 + 2x$$. 5. **Explanation:** We apply the power rule to each term separately and then sum the results. Final answer: $$\boxed{\frac{dy}{dx} = 4x^3 + 6x^2 + 2x}$$