Quotient Function MnemonicDate: 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/ |
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