Originally Posted by

**chella182** Okay, this is part of a bigger question, but you don't need to know that. I just can't quite seem to get this right. I've got this function $\displaystyle l$...

$\displaystyle l=3n\ln{(\bar{x}_{g})}-n\ln{6}-4n\ln{\theta}-\frac{n\bar{x}}{\theta}$

...and I want to differentiate with respect to $\displaystyle \theta$. So collecting the terms that don't depend on $\displaystyle \theta$ together as one general constant I get...

$\displaystyle l=K-4n\ln{\theta}-\frac{n\bar{x}}{\theta}$

Looks simple, and I got an answer, but, ideally, when I find the second derivative I need it to be quite obviously negative (so that the answer I get when solving the first derivative equal to 0 is a maximum of the function), which it isn't, which is making me think that I've done something wrong. Might be worth me pointing out that $\displaystyle n$ and $\displaystyle \bar{x}$ are also constants, so they don't affect the differentiating; just make it look rank.

Any ideas?