Miscellaneous Exercises 5: Differentiation Mastery | 综合练习 5：微分（求导）精练

📚 Miscellaneous Exercises 5: Differentiation Mastery | 综合练习 5：微分（求导）精练

This article walks through the complete set of skills assessed in the miscellaneous exercises that close Chapter 5 of the AQA A-Level Mathematics pure content. For most AQA teaching schemes, Chapter 5 centres on differentiation, so the mixed questions at the end test your ability to combine first principles, the power rule, tangents and normals, stationary points, and real-world rates of change. Tackling them in exam-style conditions is the single best way to turn the rules into fluent problem-solving.

本文系统梳理 AQA A-Level 数学纯数部分第五章综合练习所考查的全部技能。对大多数 AQA 教学安排而言，第五章以微分（求导）为核心，因此章末的混合题要求你综合运用第一原理、幂法则、切线与法线、驻点以及实际变化率。在贴近考试的条件下完成这些题目，是把法则转化为熟练解题能力的最佳途径。

1. Core Differentiation Rules | 核心求导法则

Every differentiation problem rests on a small set of rules. Make sure you can quote each rule from memory and apply it without hesitation, because the miscellaneous exercises deliberately mix them within a single question.

所有求导问题都建立在少数几条法则之上。请确保你能默写并熟练运用每一条法则，因为综合练习会故意在同一道题中混用这些法则。