### The derivative song

#### Tom Lehrer

*(To the tune of "There'll Be Some Changes Made.")*

*Introductory Dialog, spoken by the Professor:*

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:

*The Derivative Song*

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*.