"The Derivative Song"
Words by Tom Lehrer
copyright (c) 1951
Tune: “There’ll Be Some Changes Made”, by W. Benton Overstreet

This recording is posted here with permission from Tom Lehrer, Prof. Norman Ramsey (who made the recording), and all the cast members who are still living. You are encouraged to download it for your own use, and to notify others of the URL (web address) for this page, or the more general URL of this site.

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Sung by the whole cast, piano by Tom Lehrer. Technical notes on the recording.

Explanation of the math in this song

Introductory Dialog: (spoken by the "Professor", played by Lewis M. Branscomb)
To cover that great theory* would be my fondest hope,
Were it not that of this course it's far beyond the scope,.
This brings us to the question, though,
Of how much math you ought to know:
Most of it is inconsequential,
But the derivative is essential.
But you oughtn't have trouble, ought you?
If you remember that song I taught you:

*i.e. Relativity, referring to the previous song

The Derivative Song:
You take a function of x and you call it y,
Take any x₀ that you care to try,
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.

These lyrics were published in American Mathematical Monthly, vol.81, p. 490 (1974).

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