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

This work is in the public domain worldwide because it has been so released by the copyright holder.