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Math Help - differentiation

  1. #1
    Newbie
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    Dec 2010
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    differentiation

    okay im really struggling with this. how would i differentiate the function

    y=1
    ---
    ln (x)

    ive tried it a couple times but cant quite get it...can someone please help?!?
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  2. #2
    Senior Member
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    Dec 2010
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    I'm guessing you mean

     \frac{d}{dx} \lparen\frac{1}{ln(x)}\rparen

    Do you know how do differentiate  \frac{1}{x} ?

    Use the chain rule

     \frac{d}{dx} \lparen\frac{1}{u}\rparen = -\frac{1}{u^2} \frac{du}{dx}

    In this case
     \frac{d}{dx} \lparen\frac{1}{ln(x)}\rparen = -\frac{1}{(ln(x))^2} \frac{d(ln(x))}{dx}
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  3. #3
    Junior Member eddie2042's Avatar
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    I'm assuming you mean y = \frac{1}{\ln(x)}.

    You can rewrite this as y = (\ln(x))^{-1} and apply the chain rule


     \frac{dy}{dx} = -(\ln(x))^{-2}\frac{1}{x} =  -\frac{(\ln(x))^{-2}}{x} = \frac{1}{x(\ln(x))^{2}}
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