Module 2 — Mathematics Extended Part

Find the derivative of $$f(x) = 3x^2 + 2x - 5$$.

Evaluate ( \int x e^2x , dx ).

If ( y = x^\sin x ), find ( \fracdydx ). mathematics extended part module 2

The Extended Part of HKDSE Mathematics is divided into two modules: M1 (Calculus and Statistics) and M2 (Algebra and Calculus). Find the derivative of $$f(x) = 3x^2 + 2x - 5$$

| Topic | Key Concepts | |-------|--------------| | | Formal definition (intuitive), sandwich theorem, continuity of functions | | Differentiation | First principles, product/quotient/chain rules, implicit differentiation, logarithmic differentiation | | Applications of Derivatives | Curve sketching, tangent/normal lines, optimization, rate of change, L’Hôpital’s rule | | Indefinite & Definite Integration | Standard integrals, substitution, integration by parts, trigonometric integrals | | Applications of Integration | Area between curves, volume of solids of revolution (disk/washer/shell methods) | | Advanced Calculus Topics | Improper integrals, numerical methods (trapezoidal rule – basic) | The Extended Part of HKDSE Mathematics is divided