The Derivative Song
- Words
- Tom Lehrer
- Music
- “There’ll be Some Changes Made” (Public domain) by W. Benton Overstreet (original lyrics by Billy Higgins)
Accompanying mathematical notation for the lyrics, as appears in Tom Lehrer’s website
| Lyrics |
Caption on screen |
| You take a function of x and you call it y |
y = f(x) |
| Take any x-nought that you care to try |
y0 = f(x0) |
| You make a little change and call it delta x |
δx = x − x0 |
| The corresponding change in y is what you find nex’ |
δy = y − y0 |
| And then you take the quotient and now carefully |
δy/δx = (y − y0)/(x − x0) |
| Send delta x to zero, and I think you’ll see |
δx → 0 |
| That what the limit gives us, if our work all checks, |
limx → 0δy/δx = dy/dx |
| Is what we call dy/dx |
dy/dx |
| It’s just dy/dx. |
|
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---
author: Tom Lehrer
base-url: "https://tomlehrersongs.com/"
date: 2020-10-27
pdf-url: "https://tomlehrersongs.com/wp-content/uploads/2018/12/the-derivative-song.pdf"
title: The Derivative Song
transcription: Gaius Julius Caesar
---