Mastering Differentiation for Edexcel A-Level Pure Maths | 精通爱德思 A-Level 纯数学微分

📚 Mastering Differentiation for Edexcel A-Level Pure Maths | 精通爱德思 A-Level 纯数学微分

Differentiation is one of the most heavily examined topics in Edexcel A-Level Pure Mathematics. It underpins applications such as gradients, tangents, normals, stationary points, optimisation and modelling. This article consolidates the key rules, common pitfalls and exam-style strategies you need to master.

微分是爱德思 A-Level 纯数学中考查频率最高的核心专题之一。它是梯度、切线、法线、驻点、优化与建模等应用的基础。本文整合关键法则、常见错误与真题风格解题策略，帮助你全面掌握。

1. First Principles and Basic Rules | 第一原理与基本求导法则

The derivative is defined by the limit f′(x) = lim_h→0 [f(x+h) − f(x)] / h. In the exam, you may be asked to prove the derivative of a simple function from first principles, especially for polynomials such as x² or x³. Always show the expansion, simplify, and then let h approach zero.

导数由极限 f′(x) = lim_h→0 [f(x+h) − f(x)] / h 定义。考试中可能要求从第一原理证明简单函数的导数，尤其是 x² 或 x³ 等多项式。务必展示展开、化简，再令 h 趋近于零。

f′(x) = lim_h→0 [f(x+h) − f(x)] / h

Memorise the standard results: d/dx xⁿ = n xⁿ⁻¹, d/dx eˣ = eˣ, d/dx ln x = 1/x, d/dx sin x = cos x, d/dx cos x = −sin x and d/dx tan x = sec²x. For constant multiples and sums, differentiate term by

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