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Homework Help: Derivative help

  1. Feb 18, 2009 #1
    1. The problem statement, all variables and given/known data
    (1/2)t^2[(2[tex]\sqrt{t}[/tex])-(1/[tex]\sqrt{t}[/tex])]

    2. Relevant equations



    3. The attempt at a solution

    No matter what I do I get the wrong answer
    Things I have tried:
    -Expanding the problem, then with the derivatives use the product rule (f)(g') + (g)(f')
     
  2. jcsd
  3. Feb 18, 2009 #2

    Tom Mattson

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    Let's see what you did. Then we can point out where you're going wrong.
     
  4. Feb 18, 2009 #3
    =(1/2)t^2[(2t^(1/2)) - (t^(-1/2))]
    =t^(5/2) - (1/2)^(3/2)
    Use product rule

    = ((5/2)t^(3/2))*((-1/2t)^(3/2)) + ((-3/4t)^(1/2))*(t^(5/2))
    =(-5/4)t^3 + (-3/4)t^3
    = -7/4t^3

    Evidently wrong.

    The correct answer on the sheet is [([tex]\sqrt{t}[/tex](10t-3)/(4)]
     
  5. Feb 18, 2009 #4

    Tom Mattson

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    That should be [itex]t^{5/2}-\frac{1}{2}t^{3/2}[/itex] (you're missing the [itex]t[/itex] in the second term).

    Why? You don't have a product anymore! Just differentiate term by term.
     
  6. Feb 18, 2009 #5
    What do i do then? ;s

    I'm stuck with t^(5/2) - (1/2)t^(3/2)
     
  7. Feb 18, 2009 #6

    Tom Mattson

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    Just differentiate term by term.

    Surely you know how to differentiate [itex]at^n[/itex] with respect to [itex]t[/itex], right? :confused:
     
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