Mastering Differentiation for Edexcel A-Level Maths | Edexcel A-Level 数学微分核心突破

📚 Mastering Differentiation for Edexcel A-Level Maths | Edexcel A-Level 数学微分核心突破

Differentiation is a central topic in Edexcel A-Level Mathematics, appearing in Pure 1, Pure 2 and Pure 3. It is the tool we use to understand how a function changes at an instant, and it underpins many applications such as curve sketching, optimisation and kinematics. This revision note walks through the key rules, standard derivatives and exam applications, with paired explanations in English and Chinese to help you revise efficiently.

微分是 Edexcel A-Level 数学的核心主题，出现在 Pure 1、Pure 2 和 Pure 3 中。我们用微分来理解函数在某一瞬间的变化方式，它是曲线作图、最优化和运动学等应用的基础。本篇复习笔记梳理关键法则、标准导数与考试应用，并采用中英对照讲解，帮助你高效复习。

1. What Differentiation Measures | 微分度量什么

The derivative of a function f(x) at a point x tells you the gradient of the tangent to the curve y = f(x) at that point. It measures the instantaneous rate of change of y with respect to x. If the derivative is positive, the function is increasing at that point; if negative, it is decreasing.

函数 f(x) 在点 x 处的导数表示曲线 y = f(x) 在该点切线的斜率。它度量 y 对 x 的瞬时变化率。如果导数为正，函数在该点递增；如果为负，则递减。

f'(x) = lim (h → 0) [f(x + h) – f(x)] / h

The notation dy/dx, f'(x), and y’ all mean the same thing. Edexcel exams use all three, so you should be comfortable switching between them.

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

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