微分

• Reading: びぶん
• Romaji: bibun
• Kanji breakdown: 微 (bi) — minute, tiny, infinitesimal; 分 (bun) — divide, portion
• Pronunciation: /bi.bɯn/

Meaning

Differentiation; differential calculus. The mathematical operation of finding the derivative of a function, expressing the instantaneous rate of change.

A core concept in mathematics and physics, 微分 pairs with 積分 (integration) to form the two pillars of calculus. Used extensively in physics, engineering, and economics to model rates of change, velocity, acceleration, and optimisation. The verbal form 微分する (Group 3) is common in academic writing and lectures.

Examples

1. 物理学では速度を求めるために位置を時間で微分する。 In physics, position is differentiated with respect to time to find velocity.
2. この関数の微分を求めてから、グラフの傾きを確認してください。 Please find the derivative of this function and then check the gradient of the graph.
3. 微分積分学はニュートンとライプニッツによって独立に発展した。 Differential and integral calculus was independently developed by Newton and Leibniz.

Usage Guide

Context: mathematics, physics, engineering

Tone: analytical

Origin & History

Coined during the Meiji-era translation of Western mathematics. 微 means minute or tiny, and 分 means to divide — reflecting the concept of infinitesimally small divisions that underpin the derivative.

Cultural Context

Era: Meiji–Modern

Generation: Adults (university+)

Social background: Academic/Scientific