second derivative

二阶导数

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

Translation evidence: Literature usage

Meaning in context

If f is differentiable near a and f' is differentiable at a, the second derivative f''(a) is the derivative of f' there.

若 f 在 a 附近可导且其导函数 f' 在 a 处可导，则 f' 在该点的导数称为 f 的二阶导数。

Example

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

Usage and distinctions

Two derivatives need not imply a continuous second derivative.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Michael Taylor — Introduction to Analysis in One Variable§4.1, equation (4.1.43) · 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§4 高阶导数 · Checked 2026-10-14
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