Find the derivative of f(x) = x³ + 2x using the definition and rules. Using the power rule: d/dx(x³) = 3x² and d/dx(2x) = 2. So f'(x) = 3x² + 2. Check with the definition at x = 1: f'(1) = 3(1)² + 2 = 5. Now integrate f'(x) back: ∫(3x² + 2)dx = x³ + 2x + C ✓ (differentiation and integration undo each other).