Tom Lehrer: Author Lyric Sheets
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Public-domain lyrics

The Derivative Song (dy/dx)

Tom Lehrer

Nine compact lines take a changing function toward the limiting ratio called a derivative.

Tom Lehrer: Author Lyric Sheets Text 4 Undated text
Public domainMathematicsCalculusTeachingPlayfulCurious
Complete public-domain lyrics

The lyric follows a function through a small change in x, a corresponding change in y, and the limiting quotient. This is the complete nine-line first-page text. Page two repeats the words with screen-caption equations; those captions are not extra lyrics. The sheet credits the musical setting to There'll Be Some Changes Made by W. Benton Overstreet and separately identifies original lyricist Billy Higgins on page two. Only Lehrer's new words are displayed.

Verse 1

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.

Credits

Written by Tom Lehrer

Words by Tom Lehrer, released into the public domain by the author. This is the author-published text edition, not a transcription of a particular performance.

Source & text edition

Author-published lyric sheet · original English words

Tom Lehrer's November 26, 2022 declaration relinquishes copyright in lyrics he wrote. It does not grant rights to third-party music, photographs or album artwork. This edition uses only his words.

Read the author’s lyric sheet (PDF)

View copyright evidence · Author’s public-domain declaration

Retrieved 2026-09-08. Line spacing and section labels are adapted for reading. The displayed text follows the linked edition. Editorial notes and abstract artwork are by 52lyrics.
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