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F(t) = square root of 3t+2 / 4t-3

  1. Jun 29, 2005 #1

    kim

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    Need to find the derivative of:

    f(t) = square root of 3t+2 / 4t-3

    please help.
     
  2. jcsd
  3. Jun 29, 2005 #2

    Hurkyl

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    Staff Emeritus
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    What have you tried?
     
  4. Jun 29, 2005 #3
    is this sqrt{3t+2 / 4t-3} or sqrt{3t+2} / 4t-3
     
  5. Jul 1, 2005 #4
    Well, decide whether
    And the Quotient Rule will help you solve this problem~!:smile:!
    [tex] \frac{d}{{dt}}\left[ {\frac{{f\left( t \right)}}{{g\left( t \right)}}} \right] = \frac{{f'\left( t \right)g\left( t \right) - f\left( t \right)g'\left( t \right)}}{{\left[ {g\left( t \right)} \right]^2 }} [/tex]
     
    Last edited: Jul 1, 2005
  6. Jul 1, 2005 #5
    Or the product rule... :)

    [tex]\sqrt{3t+2}*(4t-3)^{-1}[/tex]
     
  7. Jul 1, 2005 #6
    or do implicit differentiation:
    let y = sqrt(3t + 2)/(4t-3)
    and then (4t-3)y = sqrt(3t+2)
     
  8. Jul 1, 2005 #7
    Well, touche then. I'll think of something more clever later...
     
  9. Jul 1, 2005 #8
    while you are thinking of something else...here's another idea:
    logarithmic differentiation
    lny = (1/2)ln(3t+2) - ln(4t-1)
     
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