Derivative of fraction without quotient rule

  • Thread starter mark1
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  • #1
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The following problem appears in my textbook (before it discusses the quotient or product rule, so those rules cannot be used for the answer):

Find the derivative of the function: [tex]\frac{x^3-3x^2+4}{x^2}[/tex]

I brought the denominator to the top and multiplied it out to get [tex]{x-3+4x^-2}[/ltex]. I then took the derivative of that to get [tex]{1-0-8x^-3}[/tex], which can be simplified to [tex]\frac{-7}{x^3}[/tex].

However, in the back of my book, the answer is given as [tex]\frac{x^3-8}{x^3}[/tex].

Please enlighten me as to where i went wrong.
 

Answers and Replies

  • #2
1,036
1
Your arithmetic:
[tex]1 - \frac{8}{x^3} \neq \frac{-7}{x^3}[/tex]
 
  • #3
27
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Thanks! For some reason, i did the calculus right but messed up on the algebra. :redface:
 
  • #4
1,036
1
It happens. :smile:
 

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