1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
    Vu'-Uv'/v^2

    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
    9x-8(sqrt(3x-4))/6x-8

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

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

    HallsofIvy

    User Avatar
    Staff Emeritus
    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
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted