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Math Help - Differentiating natural log

  1. #1
    Newbie
    Joined
    Aug 2009
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    15

    Differentiating natural log

    Differentiate f and find the domain of f

    f(x) = \sqrt{1-ln x}

     f'(x) = 1/2 (1 - ln x) (1 - ln x)'

           = [(1-ln x)/2] [-1/x]

           = - [1 - ln x/2x]

    I know I'm doing something wrong, I did a few of these before but I'm not getting the chain rule being in here and what not. The answer SHOULD be

    \frac{-1}{2x\sqrt{1-ln x}}

    Can anyone help here?
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  2. #2
    Member
    Joined
    Nov 2009
    Posts
    186
    The derivative of the natural log is \frac{1}{x}

    f(x)=\sqrt{1-lnx}

    f(x)=({1-lnx})^{\frac{1}{2}}

    f(x)'=\frac{1}{2}({1-lnx})^{\frac{-1}{2}}*\frac{-1}{x}

    Now just do some simplication

    \frac{-1}{2x\sqrt{1-lnx}}
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