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 xnought that you care to try 
y_{0} = f(x_{0}) 
You make a little change and call it delta x 
δx = x − x_{0} 
The corresponding change in y is what you find nex’ 
δy = y − y_{0} 
And then you take the quotient and now carefully 
δy/δx = (y − y_{0})/(x − x_{0}) 
Send delta x to zero, and I think you’ll see 
δx → 0 
That what the limit gives us, if our work all checks, 
lim_{x → 0}δy/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All the lyrics on this website, whether published or unpublished, copyrighted or uncopyrighted, may be downloaded and used in any manner whatsoever, without requiring any further permission from me or any payment to me or to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.
Note: This website will be shut down on December 31, 2024, so if you want to download anything, don’t wait too long.

author: Tom Lehrer
baseurl: "https://tomlehrersongs.com/"
date: 20201027
pdfurl: "https://tomlehrersongs.com/wpcontent/uploads/2018/12/thederivativesong.pdf"
title: The Derivative Song
transcription: Gaius Julius Caesar
