This is a differentiation problem that I stumbled across while trying to calculate log-likelihood estimate, so it is related to statistics.

I'm having problems with the differentiation below

http://www.geocities.com/arkayz_bible/optimization/0512471831.png

I can see how the http://www.sosmath.com/CBB/latexrender/pictures/d970bf5c90e7a30a5aaf61b50fad4d8e.gif is obtained using the product rule, but I don't see how the term after that, http://www.sosmath.com/CBB/latexrender/pictures/548736e3008025c73ed5fa915a75bc22.gif, was obtained. Shouldn't that term be http://www.sosmath.com/CBB/latexrender/pictures/3a6ee1aca186925a5b19ed1e44030c7e.gif instead? See how I got this term (http://www.geocities.com/arkayz_bible/scanned-book-three/98.png). What have I done wrong?

Macro,

You are differentiating with respect to sigma^2, not sigma. It would be easier if you let t=sigma^2 in the logL, and get the partial derivative wrt t. :)