# **Exercise Questions** All questions in this exercise are listed below. Click on a question to view its solution. --- # **Key Concepts** This exercise focuses on the following concepts: - Power Rule for differentiation - Product Rule for products of functions - Quotient Rule for rational functions - Chain Rule for composite functions - Evaluating derivatives at specific points - Differentiation of polynomial and rational functions --- # **Important Formulas** Below are the key formulas used in this exercise: **Power Rule:** $$\frac{d}{dx}(x^n) = nx^{n-1}$$ **Product Rule:** $$\frac{d}{dx}[u(x)v(x)] = u'(x)v(x) + u(x)v'(x)$$ **Quotient Rule:** $$\frac{d}{dx}\left[\frac{u(x)}{v(x)}\right] = \frac{u'(x)v(x) - u(x)v'(x)}{[v(x)]^2}$$ **Chain Rule:** $$\frac{d}{dx}[f(g(x))] = f'(g(x)) \cdot g'(x)$$ --- # **Summary** This exercise covers fundamental differentiation techniques for algebraic functions. Questions 1–10 focus on applying the power, product, and quotient rules to find derivatives of polynomials and rational functions. Questions 11–13 introduce the chain rule for composite functions in denominators and squared terms. Questions 14–17 combine differentiation with evaluation at specific points. Key strategies include simplifying expressions before differentiating when possible (e.g., Q10, Q14) and carefully tracking signs and exponents when applying the quotient rule. Watch for opportunities to expand products before differentiating as an alternative to the product rule.