Poem to help you remember the quotient rule (created 2010-11-26).
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I was working on some derivatives then involved a fraction, and the formula is a bit tricky to remember. There was a short poem that I learned a long time ago for the derivative of a fraction, and I can't find it anywhere on the Internet. There are some variants that are close, but nothing quite like the poem I remember. Everything important has to be found somewhere on the Internet, so I am posting the poem here. If anyone can attribute this poem to the original source, please let me know.
If quotient rule you wish to know,
It's lo d hi less hi d lo.
Draw the line and down below
Denominator squared will go.
There's a variation like this based on the Old McDonald song,
Lo-de-hi less hi-de-lo EIEIO
Then draw the line and down below EIEIO
With a dx here and a dy there Here a slope, yes there's hope, you can cope
Denominator squared will go EIEIO
but it's not nearly as good as the version I remember.
Here's the algebraic version:
Here's how it corresponds to the poem:
Here's the recent example I used it on.
The derivative of exp(x) is exp(x) and the derivative of 1+exp(x) is exp(x). So there is a lot of repetition going on here. But see if you can follow the logic.
For the record, this simplifies to