Mastering the Chain Rule with Worked Example 4.5.4 | 链式法则精讲：例题4.5.4详解

📚 Mastering the Chain Rule with Worked Example 4.5.4 | 链式法则精讲：例题4.5.4详解

Welcome to this revision guide from TutorHao. In this article we will dissect Example 4.5.4 from the AQA A-Level Mathematics specification. We will work through the problem step by step, explaining every algebraic manipulation and linking it to exam-style questions. This example focuses on the chain rule, one of the most important differentiation techniques in the pure mathematics module.

欢迎查阅 TutorHao 的复习指南。在本文中，我们将深入解析 AQA A-Level 数学考纲中的例题4.5.4。我们会一步一步地推导问题，解释每一步代数变形，并将其与考试型题目联系起来。本例题聚焦于链式法则——纯数模块中最核心的求导技巧之一。

1. Problem Statement | 例题陈述

Example 4.5.4 presents a classic differentiation problem from the pure mathematics section of AQA A-Level. The function is y = (3x² − 4x + 2)⁶ and we are asked to find dy/dx. This type of question appears regularly in Paper 1 and Paper 2 of the AQA specification. It tests not only your knowledge of differentiation rules but also your ability to work systematically through a composite function.

例题4.5.4是 AQA A-Level 纯数部分的一道经典求导问题。函数为 y = (3x² − 4x + 2)⁶，要求求 dy/dx。这类题目经常出现在 AQA 考纲的 Paper 1 和 Paper 2 中。它不仅考查你对求导法则的掌握，还考查你是否能系统地对复合函数进行逐步求解。

2. Underlying Rule: The Chain Rule | 前置知识：链式法则

Before we solve the example, let us recall the chain rule. If y = (u(x))ⁿ, then dy/dx = n(u(x))ⁿ⁻¹ du/dx. Equivalently, if y = f(g(x)), then dy/dx = f′(g(x)) ·

Published by TutorHao | A-Level Mathematics Revision Series | aleveler.com

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