Tom Lehrer — The Derivative Song

[Introduction: Spoken] 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: [Verse 1] You take a function of x and call it y Take any x naught that you care to try You make a little change and call it Delta X The corresponding change in y is what you find next And then you take the quotient and now carefully Send out x to zero and I think you'll see That what the limit gives us if our limit checks Is what we call dy dx Its just dy dx.