The Derivative Song
- Tom Lehrer
- “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
||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
|It’s just dy/dx.
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author: Tom Lehrer
title: The Derivative Song
transcription: Gaius Julius Caesar