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Math Help - differentiate and find the domain of f

  1. #1
    DBA
    DBA is offline
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    differentiate and find the domain of f

    Hello, I was able to do part one but have problem finding the domain

    f(x) = x / [1-ln(x-1)]

    The solution says:

    x<=1 and ln(x-1) = 1

    x<=1 and ln(x-1) = ln e

    x<=1 and x-1 = ln e
    --> Here I do not understand how to get from ln(x-1) to x-1

    x<=1 and x = (e + 1) --> I do not get this step too

    Can someone explain that to me. Thanks
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by DBA View Post
    Hello, I was able to do part one but have problem finding the domain

    f(x) = x / [1-ln(x-1)]

    The solution says:

    x<=1 and ln(x-1) = 1

    x<=1 and ln(x-1) = ln e

    x<=1 and x-1 = ln e
    --> Here I do not understand how to get from ln(x-1) to x-1

    x<=1 and x = (e + 1) --> I do not get this step too

    Can someone explain that to me. Thanks
    f'(x)=\frac{1\cdot[1-\ln(x-1)]-x\cdot\frac{-1}{x-1}}{[1-\ln(x-1)]^2}=\frac{(x-1)[1-\ln(x-1)]+x}{(x-1)[1-\ln(x-1)]^2}

    Note that

    \ln(x-1) implies x>1

    And the denominator cannot be equal to zero, which mens that

    1-\ln(x-1)\neq0

    But

    1-\ln(x-1)=0 occurs when

    x-1=e

    x=e+1

    therfore, the domain of the f prime is

    All x>1\neq{e+1}
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