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Math Help - What is f'(e) for f(x) = x/(lnx)

  1. #1
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    What is f'(e) for f(x) = x/(lnx)

    I said, using the quotient rule,

    f'(x)[1(lnx) - x(1/x)]/(lnx)^2 = lnx - 1

    so f'(e) = (lne - 1) / (lne)^2 = 1-1/1 = 0/1 = 0
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  2. #2
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    Quote Originally Posted by satx View Post
    I said, using the quotient rule,

    f'(x)[1(lnx) - x(1/x)]/(lnx)^2 = lnx - 1 <... ?

    so f'(e) = (lne - 1) / (lne)^2 = 1-1/1 = 0/1 = 0
    so f'(x)=\frac{\log(x)-1}{\log^2(x)}
    which means f'(e)=\frac{\log(e)-1}{\log^2(e)}=0
    you're right
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