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Help with Logarithmic Differentiation

  1. Jul 16, 2012 #1
    1. The problem statement, all variables and given/known data
    y = [2x + 1]^5 * [(x^4) - 3]^6


    2. Relevant equations
    I take the derivative of the natural log of both sides:

    (y' / y) = [(10 ln(2x + 1)^4) / (2x + 1)] + [(24x^3 ln(x^4 - 3)^5) / (x^4 - 3)]

    then I multiply both sides by the original function:

    y' = [((10 ln(2x + 1)^4) / (2x + 1)) + ((24x^3 ln(x^4 - 3)^5) / (x^4 - 3))] * [(2x + 1)^5 * ((x^4) - 3)^6]

    My book, however, says the answer is:

    y' = [(10 / (2x + 1)) + (24x^3 / (x^4 - 3))] * [(2x + 1)^5 * ((x^4) - 3)^6]

    ^ i.e., the same thing without the logs.

    Could someone please explain what I did wrong, or where I might have gone wrong?


    3. The attempt at a solution
    What you see above.
     
  2. jcsd
  3. Jul 16, 2012 #2

    SammyS

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    It's helpful to do the problem in steps.

    What did you get for ln(y) ?

    Then, what did you get for the derivative of that result?
     
  4. Jul 16, 2012 #3
    I got ln(y) for ln(y), I'm not sure I understand the first question.

    The derivative of that I got:

    (1 / y)(y')
     
  5. Jul 16, 2012 #4
    I think that you took your derivitives wrong.

    I see that you broke it up into the sum of two logs, but remember that they are of the form ln(u^n) and not of the form ln(u)^n.
     
  6. Jul 16, 2012 #5
    I use chain rule on each of those logs; should I not?
     
  7. Jul 16, 2012 #6
    Ah, forget I asked anything. I understand what I did wrong. Thanks anyway.
     
  8. Jul 16, 2012 #7

    SammyS

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    If y = [2x + 1]5 * [(x^4) - 3]6, then ln(y) = __?__ .
     
  9. Jul 17, 2012 #8
    Is there a reason you didn't apply the relationship for the derivative of the product of two functions? Did the question constrain you to use logarithmic differentiation?
     
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