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Homework Help: Find the derivative of the question

  1. Mar 16, 2013 #1
    1. The problem statement, all variables and given/known data

    (9x-8)/ 2(sqrt(3x-4))

    2. Relevant equations

    i.e. quotient rule

    3. The attempt at a solution
    I get
    V=2(sqrt(3x-4) u=9x-8
    V'=3((3x-4)^-1.5) u'=9

    When I put this into the equation and solve I get

    But the answer is 3(9x-16)/4((3x-4)^1.5)

    Help Please?
  2. jcsd
  3. Mar 16, 2013 #2


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    Science Advisor

    With v= 2sqrt(3x- 4)= 2(3x- 4)^1/2, v'= 3(3x- 4)^-(1/2)= 3(3x- 4)^(.5-1)= 3(3x- 4)^-.5, not "-1.5". That's your basic error.

    So u'v- uv'= 9(2(3x-4)^1/2)- (9x- 8)(3(3x-4)^-1/2
    To combine those two square roots, use the fact that (3x-4)^1/2= (3x- 4)(3x-4)^-1/2 so we can factor (3x- 4)^-1/2 out: (3x-4)^-1/2(18(3x- 4)- 3(9x- 8))= (3x-4)^-1/2(54x- 72- 27x+ 24)= (3x- 4)^-1/2(27x- 48)= (3x- 4)^-1/2(3)(9x- 16).

    Can you finish?
    By the way, with that power in the denominator, so you will need to use the chain rule, anyway, it might be simpler to write the function as (1/2)(9x- 8)(3x-4)^-1/2 and use the product rule rather than the quotient rule.
  4. Mar 16, 2013 #3
    Writing fractions without LaTex should be punishable by death
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