Songs and Lyrics (Lehrer)/The Derivative Song (dy/dx)

by Thomas Andrew Lehrer

The Derivative Song (dy/dx)

words by Tom Lehrer
music:	"There'll Be Some Changes Made" by W. Benton Overstreet (1921) (public domain)

You take a function of x and you call it yTake any x-nought that you care to tryYou make a little change and call it delta xThe corresponding change in y is what you find nex'And then you take the quotient and now carefullySend delta x to zero, and I think you'll seeThat what the limit gives us, if our work all checks,Is what we call dy/dx,It's just dy/dx.

The Derivative Song

words by Tom Lehrer
music:	"There'll Be Some Changes Made" (public domain) by W. Benton Overstreet (original lyrics by Billy Higgins)

	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	$y_{0}=f(x_{o})$
You make a little change and call it delta-x	$\Delta {x}=x-x_{0}$
The corresponding change in y is what you find nex'	$\Delta {y}=y-{y_{0}}$
And then you take the quotient and now carefully	${\frac {\Delta {y}}{\Delta {x}}}={\frac {y-y_{0}}{x-x_{0}}}$
Send delta-x to zero and I think you'll see	$\Delta {x}\to 0$
That what the limit gives us if our work all checks	$\lim _{\Delta {x}\to 0}{\frac {\Delta {y}}{\Delta {x}}}$
Is what we call dy/dx	$\lim _{\Delta {x}\to 0}{\frac {\Delta {y}}{\Delta {x}}}={\frac {dy}{dx}}$
It's just dy/dx	${\frac {dy}{dx}}$

The Derivative Song (dy/dx)

words by Tom Lehrer
music:	"There'll Be Some Changes Made" by W. Benton Overstreet (1921) (original lyrics by Billy Higgins)

You take a function of x and you call it yTake any x-nought that you care to tryYou make a little change and call it delta xThe corresponding change in y is what you find nex'And then you take the quotient and now carefullySend delta x to zero, and I think you'll seeThat what the limit gives us, if our work all checks,Is what we call dy/dx,It's just dy/dx.

Note: should be played as