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Math Help - derivative trouble

  1. #1
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    derivative trouble

    Alright, so I am doing this set of problems, and the answers are jumbled so we can tell that if we got the right answer (if we did it right) I got every other problem right on this sheet so I know what the answer is supposed to be. Here is the problem.

    what is the derivative of (ln(x))/(3x^2)

    I take the derivative of 3x^2 and multiply that by lnx, subtract deriv of lnx * 3x^2 and put all that over (3x^2)^2 I keep on coming up with (3-6lnx)/9x^3... but the right answer is (1-2x)/(3x^3)

    Am I missing some identity or am I doing something really wrong?

    Thank you
    Chris
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  2. #2
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    San Diego
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    Quote Originally Posted by omniftw View Post
    Alright, so I am doing this set of problems, and the answers are jumbled so we can tell that if we got the right answer (if we did it right) I got every other problem right on this sheet so I know what the answer is supposed to be. Here is the problem.

    what is the derivative of (ln(x))/(3x^2)

    I take the derivative of 3x^2 and multiply that by lnx, subtract deriv of lnx * 3x^2 and put all that over (3x^2)^2 I keep on coming up with (3-6lnx)/9x^3... but the right answer is (1-2x)/(3x^3)

    Am I missing some identity or am I doing something really wrong?

    Thank you
    Chris
    You are right, they meant to say \frac{1-2 \ln x}{3x^3}, but just forgot to put in the natural log symbol.
    If you reduce your own answer by dividing the top and bottom by 3, what I mean would become apparent.
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  3. #3
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    Dec 2007
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    Thank you very much for your reply.

    I now understand where it came from YOu were a big help.

    Chris
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