1. ## 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

2. Originally Posted by omniftw
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.