# The Derivative Song (dy/dx)

The Derivative Song (dy/dx)  (1951)
by Thomas Andrew Lehrer

A recording of this song is available here.

The Derivative Song (dy/dx)

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

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.

THE DERIVATIVE SONG

words by Tom Lehrer

music: "There'll be Some Changes Made" (public domain)
music: "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 ${\frac {dy}{dx}}$  This work is in the public domain worldwide because it has been so released by the copyright holder.