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Math Help - Differentiating ln

  1. #1
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    Differentiating ln

    I expect this to be a simple question. However, I have never met this type of question before and have some doubts on differentiating such functions..

    Differentiate y=\frac{lnx}{2x+3}
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  2. #2
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    Quote Originally Posted by Punch View Post
    I expect this to be a simple question. However, I have never met this type of question before and have some doubts on differentiating such functions..

    Differentiate y=\frac{lnx}{2x+3}
    Yes, it is a simple question. First, it is a quotient so you need the quotient rule:
    \left(\frac{f(x)}{g(x)}\right)'= \frac{f'(x)g(x)- f(x)g'(x)}{g^2(x)}.

    You will also need to know that if f(x)= ln(x) then f'(x)= 1/x and if g(x)= 2x+3, then g'= 2.
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    Hi, I understood everything except for f(x)= ln(x) then f'(x)= 1/x
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  4. #4
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    Quote Originally Posted by Punch View Post
    Hi, I understood everything except for f(x)= ln(x) then f'(x)= 1/x
    here is a definition of the natural log function ...

    \ln{x} = \int_1^x \frac{1}{t} \, dt


    using the FTC ...

    \frac{d}{dx} \left[\ln{x} = \int_1^x \frac{1}{t} \, dt\right]

    \frac{d}{dx} \ln{x} = \frac{1}{x}
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