Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math - Questions and Answers from our Archives
_____________________________________________
Associated Topics || Dr. Math Home || Search Dr. Math
_____________________________________________

Quotient Function Mnemonic


Date: 03/11/2002 at 20:23:16
From: Ryan DeMont
Subject: Grade 12 Calculus

I get really turned around when trying to factor or expand derivatives 
of quotient functions.

Help me to differentiate the following:

x/((x^2)-4)


Date: 03/17/2002 at 16:18:24
From: Doctor Nbrooke
Subject: Re: Grade 12 Calculus

Good evening, Ryan, and thanks for writing to Dr. Math.

This is a very easy mistake to make, and one that I made quite a few 
times myself when I was in Calculus. Remember that the derivative of 
the quotient function has the form 

   (f/g)' = [g*f' - f*g']/[g^2]

However, it is much easier to remember 

   LOW DEE HIGH OVER HIGH DEE LOW OVER LOW SQUARED 

where LOW is the denonominator of the quotient and HIGH is the 
numerator. So we'll organize our functions, using your example:

LOW   x^2 - 4   DEE LOW  2x
HIGH  x         DEE HIGH 1

So we get 

(LOW DEE HIGH - HIGH DEE LOW)/(LOW SQUARED) 
= ((x^2-4) - x*2x) /(x^2-4)^2 
= (x^2 - 4 - 2x^2) / (x^2-4)^2
= (-x^2 - 4) / (x^2 - 4)^2

And there we go.  I hope this mnemonic device works for you. If you 
have any more questions, please feel free to write back.

- Doctor Nbrooke, The Math Forum
  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Calculus

Search the Dr. Math Library:


Find items containing (put spaces between keywords):
 
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

_____________________________________
Math Forum Home || Math Library || Quick Reference || Math Forum Search
_____________________________________

Ask Dr. MathTM
© 1994-2013 The Math Forum
http://mathforum.org/dr.math/