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Derivative of fraction without quotient rule

  1. Nov 19, 2004 #1
    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.
  2. jcsd
  3. Nov 19, 2004 #2
    Your arithmetic:
    [tex]1 - \frac{8}{x^3} \neq \frac{-7}{x^3}[/tex]
  4. Nov 19, 2004 #3
    Thanks! For some reason, i did the calculus right but messed up on the algebra. :redface:
  5. Nov 19, 2004 #4
    It happens. :smile:
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