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Bad differention?

  1. Sep 24, 2009 #1
    1. The problem statement, all variables and given/known data
    Differentiate using the product rule

    2. Relevant equations

    [tex](2t^2+t^{(1/3)})(4t-5)[/tex]

    3. The attempt at a solution

    [tex]h'(t) = f'(t)g(t)+f(t)g'(t)[/tex]

    [tex](4t+\frac {1}{3}t^{\frac {-2}{3}})(4t-5)+(2t^2+t^{(1/3)})(4)[/tex]
    [tex] \frac {-5}{3t^{2/3}}+24t^{2}-20t+\frac {16}{3}t^{1/3}[/tex]

    Why is this wrong?
     
    Last edited: Sep 24, 2009
  2. jcsd
  3. Sep 24, 2009 #2
    maybe your missing something in the question because the work you showed is correct.
     
  4. Sep 24, 2009 #3

    Pengwuino

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    Gold Member

    Looks right as can be.
     
  5. Sep 24, 2009 #4
    The answer in the book is much different, though:
    [tex] h'(t) = \frac {72x^{8/3} - 60x^{5/3} + 16x -5}{3x^{2/3}}[/tex]

    Something is not right :/.
     
  6. Sep 24, 2009 #5

    Pengwuino

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    Gold Member

    Those 2 answers are equal....... other then the t's all of a sudden being x's :).
     
  7. Sep 24, 2009 #6

    Dick

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    Homework Helper

    It's not that much different. 72*x^(8/3)/(3*x^(2/3)) is 24*x^2 which if I replace x by t corresponds to the 24*t^2 in your solution. Can you match the other terms up as well? They just factored the answer in a different way.
     
  8. Sep 24, 2009 #7
    Ahhhhh, that explains it! Thank you very much :).
     
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