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Math Help - simplify log derivative/distribution

  1. #1
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    simplify log derivative/distribution

    I have been having trouble trying to follow along an example of, finding the derivative of (11x)^{ln11x} .

    Using the property A^r = rlnA

    ln(f(x))= (ln11x) (ln11x)

    Now differentiate the left side, then the right side....

    Left Side: \frac{d}{dx}[ln(f(x))]= \frac{1}{f(x)}f'(x)

    Right side: \frac{d}{x}[(ln11x) (ln11x)] = \frac{2ln11x}{x}

    \frac{1}{f(x)}f'(x) = \frac{2ln11x}{x}

    multiply both sides by f(x) , to get f'(x) by itself. f'(x) = f(x)* \frac{2ln11x}{x}

    Now replcace f(x) for  (11x)^{ln11x}

    f'(x) = (11x)^{ln11x} * \frac{2ln11x}{x}

    I getting confused at this part...... how does it get to here

     = 2* 11^{ln11x}x^{ln11x-1}ln11x
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  2. #2
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    Re: simplify log derivative/distribution

    (11x)^{ln11x} = 11^{ln11x}x^{ln11x}

    So

    \frac{(11x)^{ln11x}}x= \frac{11^{ln11x}x^{ln11x}}x= 11^{ln11x}x^{ln11x-1}

    Now multiply both sides by 2ln11x and you are there.
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