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Homework Help: Find the derivative

  1. Jun 20, 2010 #1
    1. The problem statement, all variables and given/known data
    Find f' of ln[((x2+1).5) / x(2x3-1)2]


    2. Relevant equations



    3. The attempt at a solution
    I know the derivative of ln(x) is 1/x... however I don't know how to start this particular problem. I think there is a easier way to solve this without trying to solve the derivative of [((x2+1).5) / x(2x3-1)2]..?
     
  2. jcsd
  3. Jun 20, 2010 #2
    You need to use the chain rule. And I don't think there is an "easy" way to do this (i.e. a shortcut). You just need to do a lot of bookkeeping.

    Also although you are correct to say that d/dx [ln(x)] = 1/x, that does not really help since the argument of the log function is not 'x' it is a function of x. So we say that if 'u' is a function of x, then d/dx [ln(u)] = 1/u *du/dx.

    That is the chain rule applied to the natural log function.
     
  4. Jun 20, 2010 #3

    HallsofIvy

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    Use the laws of logarithms:

    [tex]\ln\left[\frac{(x^2+ 1)^{.5}}{x(2x^3-1)^2}\right]= .5 ln(x^2+ 1)- ln(x)- 2ln(2x^3- 1)[/tex]

    That's a little easier to differentiate.
     
  5. Jun 20, 2010 #4

    Mark44

    Staff: Mentor

    Before differentiating, use the properties of logs so that instead of the log of a quotient, you're working with a difference of logs. You will need to use the chain rule when you actually start differentiating.
     
  6. Jun 20, 2010 #5

    HallsofIvy

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    Wow, three responses in three minutes.

    But, this time, I got in before Mark44!!!
     
  7. Jun 20, 2010 #6
    Thanks! :)
     
  8. Jun 20, 2010 #7

    Mark44

    Staff: Mentor

    I'm having a slow day:smile:
     
  9. Jun 20, 2010 #8
    Muh hahaha! But not before me! Now somebody answer my Incomplete Gamma function question!
     
  10. Jun 21, 2010 #9
    HallsoftIvy,

    If this was the star wars univers you would be yoda and the rest of us younglings!
     
  11. Jun 21, 2010 #10

    HallsofIvy

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    How did you find out I was short and wrinkly?
     
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