Derivative rules simplify computation. (1) Sum: d/dx[f+g] = f'+g'; (2) Product: d/dx[fg] = f'g + fg'; (3) Quotient: d/dx[f/g] = (f'g - fg')/g²; (4) Chain: d/dx[f(g(x))] = f'(g) × g'(x); (5) Power: d/dx[xⁿ] = nxⁿ⁻¹. Example: f(x) = (x² + 1)(x - 3). Using product rule: f'(x) = 2x(x-3) + (x²+1)(1) = 3x² - 6x + 1. Or: f(x) = x³ - 3x² + x - 3, f'(x) = 3x² - 6x + 1. Chain rule: f(x) = (2x+1)³. f'(x) = 3(2x+1)² × 2 = 6(2x+1)². Exam tip: Choose appropriate rule. Practice: Apply multiple rules in sequence. Verify by alternate methods.