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
---