Edexcel A-Level Maths: Differentiation Rules, Tangents and Stationary Points | 爱德思 A-Level 数学：微分法则、切线与驻点

📚 Edexcel A-Level Maths: Differentiation Rules, Tangents and Stationary Points | 爱德思 A-Level 数学：微分法则、切线与驻点

Differentiation is one of the largest topics in Edexcel A-Level Pure Mathematics. It connects algebraic skills, the geometry of curves and real-world rates of change, so exam questions often combine several ideas at once.

微分是爱德思 A-Level 纯数学中最大的主题之一。它将代数技能、曲线几何和现实变化率联系起来，因此考试题经常同时综合多个知识点。

1. What Differentiation Measures | 微分度量什么

Differentiation gives the instantaneous rate of change of a function. For a graph y = f(x), the derivative f'(x) is the gradient of the tangent at any given point.

微分给出函数的瞬时变化率。对于图像 y = f(x)，导数 f'(x) 是任意给定点处切线的斜率。

If the curve rises as x increases, f'(x) is positive. If the curve falls, f'(x) is negative. A zero derivative corresponds to a horizontal tangent, which may indicate a stationary point.

如果曲线随 x 增加而上升，f'(x) 为正；如果曲线下降，f'(x) 为负。导数为零对应水平切线，这表示可能存在驻点。

This idea underpins optimisation, curve sketching and many applied problems in Edexcel examinations.

这一思想是爱德思考试中最优化、曲线作图以及许多应用问题的基础。

2. First Principles from Secant to Tangent | 从割线到切线的第一性原理

The formal definition of the derivative comes from the gradient of a chord between two nearby points on the curve y = f(x).

导数的正式定义来自曲线 y = f(x) 上两个邻近点之间弦的斜率。

If the two points have x-coordinates x and x + h, the gradient of the chord is:

如果两个点的横坐标为 x 和 x + h，则弦的斜率为：

[f(x + h) – f