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# Quick natural logarithms question! watch

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

Differentiate:

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:

However, the answer clearly says it's:

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!
2. 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.
3. 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.
4. Well I used the quotient rule ..

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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