Song by Tom Lehrer to the tune "There'll be Some Changes Made". Published in American Mathematical Monthly, 81 (1974). Reproduced here with Tom Lehrer's written permission (see this node).

You take a function of x and you call it y,
Take any x-nought that you care to try,
You make a little change and call it delta x,
The corresponding change in y is what you find nex',
And then you take the quotient and now carefully
Send delta x to zero, and I think you'll see
That what the limit gives us, if our work all checks,
Is what we call dy/dx,
It's just dy/dx.

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.

DISCLAIMER STATEMENT

I, Tom Lehrer, and the Tom Lehrer Trust 2000, hereby grant the following permission:

All the lyrics on this website, whether published or unpublished, copyrighted or uncopyrighted, may be downloaded and used in any manner whatsoever, without requiring any further permission from me or any payment to me or to anyone else.

Some lyrics written by Tom Lehrer to copyrighted music by others are included herein, but of course such music may not be used without permission of the copyright owners. (The translated songs may be found in their original languages on YouTube.)

In other words, all the lyrics herein should be treated as though they were in the public domain.

In particular, permission is hereby granted to anyone to set any of these lyrics to their own music and publish or perform their versions without fear of legal action.

This permission applies only to the lyrics on this website. Most of the music written by Tom Lehrer will be added gradually later with further disclaimers.

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```---
author: Tom Lehrer
base-url: "https://tomlehrersongs.com/"
date: 2020-10-27