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Math Help - ln function...finding value of f'(x)

  1. #1
    Senior Member polymerase's Avatar
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    ln function...finding value of f'(x)

    If f(x)=ln(ln\:x), find the value of f'(\frac{1}{e})

    Choices:

    a) -\frac{1}{e}
    b)undefined
    c) \frac{1}{e}
    d) 2e
    e) \sqrt{e}

    alright, heres where im at right now:

    1)It could be undefined because \frac{1}{e} is not in the domain of f(x)?
    2)the answer is -e and my prof made a mistake(seems unlikely since he's been doing this for 20 years)?
    3)my friend says its \frac{1}{e}?

    Can anyone confirm which is correct with justification?

    Thanks!
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  2. #2
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    Hello, polymerase!

    If f(x)\:=\:\ln(\ln x), find the value of f'\left(\frac{1}{e}\right)

    Choices: . a)\;\text{-}\frac{1}{e}\qquad b)\;\text{unde{f}ined}\qquad c)\;\frac{1}{e}\qquad d) \;2e \qquad e) \;\sqrt{e}

    I agree with your answer . . . {\color{blue}\text{b) unde{f}ined}}

    f\left(\frac{1}{e}\right) \:=\:\ln\left[\ln\left(\frac{1}{e}\right)\right] \;=\;\ln\left[\ln\left(e^{-1}\right)\right] \;=\;\ln(-1) .??

    The function does not exist at that point, so neither does its derivative.

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  3. #3
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    Quote Originally Posted by Soroban View Post
    Hello, polymerase!


    I agree with your answer . . . {\color{blue}\text{b) unde{f}ined}}

    f\left(\frac{1}{e}\right) \:=\:\ln\left[\ln\left(\frac{1}{e}\right)\right] \;=\;\ln\left[\ln\left(e^{-1}\right)\right] \;=\;\ln(-1) .??

    The function does not exist at that point, so neither does its derivative.
    Hello, I did this and used Maple to confirm. Finding the derivative of this double ln first:
    ln(ln(x)) = 1/ln(x) * 1/x
    now you sub in (1/e)
    1/ln(1/e) = 1/ln(e^-1) noting that.. ln (e^x) = x
    so = 1/ln(e^-1) = 1/-1 * 1/(1/e)
    so multiply the reciprical since your dividing by a fraction and your final answer is -e!
    Im pretty sure im right, and im matching the answer of your 20 years experience prof :P
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    i agree with Soroban. we can't take the derivative where the function is not defined

    (when i tried to evaluate the derivative in maple, it told me "invalid input...")
    Last edited by Jhevon; December 7th 2007 at 12:01 AM.
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  5. #5
    Senior Member DivideBy0's Avatar
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    Just adding my evidence to the stack, my TI gives Error: Constraint Expression Invalid
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  6. #6
    Senior Member polymerase's Avatar
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    Thank You all
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