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    pop000's Avatar
    pop000 Posts: 352, Reputation: 6
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    #1

    Dec 30, 2010, 04:44 AM
    Derivative for ln(x)
    How do I find the Derivative for the Function.


    Thanks.
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    ebaines's Avatar
    ebaines Posts: 12,131, Reputation: 1307
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    #2

    Dec 30, 2010, 12:39 PM

    The derivative of ln(x) is 1/x. I'm not sure what you're trying to get at with your formula:



    This formula is incorrect, so please clarify your question.
    pop000's Avatar
    pop000 Posts: 352, Reputation: 6
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    #3

    Dec 30, 2010, 01:59 PM
    hi. I know that the derivative of ln(x) is 1/x. but the original question was to prove that the Function ln(x)=1/x-1 has exactly 2 Solutions

    I need to find the derivative.


    hope is more clear now :)
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
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    #4

    Dec 30, 2010, 03:16 PM

    You can use the Intermediate Value Theorem and/or Rolles Theorem to prove it has two solutions.
    harum's Avatar
    harum Posts: 339, Reputation: 27
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    #5

    Dec 30, 2010, 09:40 PM
    Would like to help you but have not a slightest idea what you want to do here.

    Equations ln(x) = 1/x-1 and ln(x) = -1/(x-1) are not the same, so it gets more and more confusing.

    The first equation has only one solution, the second -- none.
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
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    #6

    Dec 31, 2010, 04:54 AM

    You can rewrite it as:

    and then try to show this has exactly two solutions.

    The thing is, it does not have two solutions.

    But, if it were , then it would have the two solutions.

    Both graphs appear below.
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    pop000 Posts: 352, Reputation: 6
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    #7

    Jan 1, 2011, 03:23 AM
    OK I will try thanks to all of you for helping.
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