derivative of a real function

导数

Analysis, Measure & PDE · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Translation evidence: Literature usage

Meaning in context

For a real function defined near a, its derivative at a is the finite limit of (f(a+h)-f(a))/h as nonzero h tends to zero.

实函数在点 a 附近有定义，若增量商 (f(a+h)-f(a))/h 在 h 趋于零时有有限极限，该极限就是 a 处的导数。

Example

For f(x)=x3f(x)=x^3, f′(2)=12f'(2)=12.

Usage and distinctions

A two-sided derivative requires agreement of the left and right limits.

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Definition sources

  1. Michael Taylor — Introduction to Analysis in One Variable§4.1, equations (4.1.1)–(4.1.3) · Checked 2026-10-14

Translation sources

  1. 中国矿业大学数学学院 — 数学分析讲义，第五章§1 导数的概念 · Checked 2026-10-14
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