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    • Thread Starter

    Hey, just a quick question regarding natural logarithms in questions in which the quotient rule is needed.

    Differentiate: \frac{1-lnx}{x^2}

    This is what I've done:

    u = 1-lnx
    v = x^2
    du/dx = -1/x
    dv/dx = 2x

    Then when I expand everything (haven't cancelled anything out yet), I get:

    \frac{-x - 2x + 2xlnx}{x^4}

    However, the answer clearly says it's:

    \frac{2lnx - 3}{x^3}

    I don't understand how they got 2lnx when -2x multiplied by -lnx should give -2xlnx. If someone can help me here, I'll be very grateful. Thank you!
    • PS Helper

    PS Helper
    There's a common factor of x on the top and bottom of your fraction. You've got the same answer effectively, but you haven't cancelled it down.

    I just did this question before. You've got to be doing OCR MEI right?

    Oh and you take a common factor of the numerator. Like nuodai said.

    Well I used the quotient rule ..

    \dfrac{x^2(-\dfrac{1}{x}) - ((1-ln(x))2x)}{x^4}\\





    Yea well you got the same answer and didn't simplify lol. Just saw it now after seeing your answer.
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Updated: October 12, 2009

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