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Product Rule Derivative Problem

  1. Nov 3, 2012 #1
    1. The problem statement, all variables and given/known data

    Use the product rule to differentiate the function:

    h(t) = √t(1-t2)

    2. Relevant equations

    d/dx[f(x)g(x)] = f(x)g'(x) + g(x)f'(x)

    3. The attempt at a solution

    (see attachment image)

    I checked the back of the textbook and my solution was wrong. The textbook says the answer is (1 - 5t2)/(2√t). What did I do wrong? How do you get this answer?
     

    Attached Files:

  2. jcsd
  3. Nov 3, 2012 #2
    Between lines 3 and 4 of your work you incorrectly simplified the first term like this:
    [tex]t^{\frac{1}{2}}(-2t)=-2\sqrt t[/tex]Otherwise, I agree with your work.
     
    Last edited: Nov 3, 2012
  4. Nov 3, 2012 #3
    Ahh good catch. You would then just do (-2t√t)(2√t) and get -4t2. Add that to 1 - t2 on the numerator and you get (1 - 5t2) / 2√t, the correct answer in the textbook. Thanks.
     
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