Differentiation Techniques for Edexcel A-Level Maths | Edexcel A-Level 数学微分技巧

📚 Differentiation Techniques for Edexcel A-Level Maths | Edexcel A-Level 数学微分技巧

This revision guide covers the core differentiation techniques required for Edexcel A-Level Mathematics, with worked ideas, exam-focused language, and common pitfalls.

本复习指南涵盖 Edexcel A-Level 数学所需的核心微分技巧，包括解题思路、考试重点及常见易错点。

1. First Principles and the Gradient Function | 第一原理与梯度函数

The derivative f'(x) measures the rate of change of a function f(x). Geometrically, it gives the gradient of the tangent to the curve y = f(x) at any point.

导数 f'(x) 衡量函数 f(x) 的变化率。从几何上看，它表示曲线 y = f(x) 在某点切线的斜率。

f'(x) = limₕ→₀ (f(x + h) − f(x)) / h

This limit may be tested directly with simple polynomials such as f(x) = x² or f(x) = x³. You must show the expansion, cancellation, and limiting process clearly.

该极限可能直接以简单多项式考查，例如 f(x) = x² 或 f(x) = x³，你需要清晰展示展开、约分和取极限的过程。

In an exam, always write the limit statement before substituting h = 0, as examiners award method marks for this structure.

考试中，在代入 h = 0 之前一定要写出极限表达式，因为阅卷人会根据这一结构给方法分。

2. The Power Rule and Basic Derivatives | 幂法则与基本导数

For any real constant n, the derivative of xⁿ is n xⁿ⁻¹. This rule works for positive integers, negative powers, and fractional powers such as √x and 1/x².

对于任意实数 n，xⁿ 的导数为 n xⁿ⁻¹。该法则适用于正整数、负整数以及分数次幂，例如 √x 和 1/x²。

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