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First derivative

  1. Feb 27, 2010 #1
    1. The problem statement, all variables and given/known data
    differentiate f(x) = [2x^(2/3)][3-4x^(1/3)]

    2. Relevant equations

    3. The attempt at a solution
    f'(x) = (4/3)(x^(-1/3))(3-4x^(1/3)) + (1/3)(-4)(x^(-2/3))
    = 4x^(-1/3)-(16/3)-((4/3)(x^(-2/3)))
    = (4/x^(1/3))-(16/3)-(4/3(x^(-2/3)))
    I'm pretty sure I've made a mistake, but I can't find it.
  2. jcsd
  3. Feb 27, 2010 #2


    User Avatar
    Gold Member

    Remember, the product rule is defined as [itex]f' = g'h + gh'[/itex]. When you used the product rule, you forgot to multiply the second term by [itex]2x^{2/3}[/itex].
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