Differentiation | 微分

📚 Differentiation | 微分

Differentiation is a core Pure Mathematics topic in Edexcel A-Level. It measures how a function changes as its input changes, giving the gradient of a curve and the instantaneous rate of change. Mastery of the rules and applications of differentiation is essential for both the Pure papers and many applied modelling problems.

微分是爱德思 A-Level 纯数学的核心主题。它衡量函数随输入变化而变化的速度，给出曲线的斜率与瞬时变化率。掌握微分法则及其应用，对纯数试卷和许多应用建模问题都至关重要。

1. First Principles and Basic Derivatives | 第一性原理与基本导数

The derivative of a function f at x is defined as the limit of the average gradient from x to x+h as h tends to zero. This gives the gradient of the tangent at a point. In symbols, for a small change h, f'(x) = lim (h → 0) [f(x + h) − f(x)] / h.

函数 f 在 x 处的导数定义为从 x 到 x+h 的平均斜率当 h 趋于 0 时的极限。它给出曲线在该点切线的斜率。记作 f'(x) = lim (h → 0) [f(x + h) − f(x)] / h。

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

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