Differentiate log likelihood

[morten23]

Hi,
Can someone help me and explain step-by-step how to partial differentiate the following log-likelihood (see picture) wrt. mu (the sign that looks like u).
Also, how to differentiate the same equation wrt. omega (the sign that looks like w).




Thank you

 

[Deleted member 4993]

Hi,
Can someone help me and explain step-by-step how to partial differentiate the following log-likelihood (see picture) wrt. mu (the sign that looks like u).
Also, how to differentiate the same equation wrt. omega (the sign that looks like w).


View attachment 15993

Thank you

If I were to do the problem, I'll first simplify (to my eye only) as follows:

\(\displaystyle l_t(\theta) \ = -\frac{1}{2} * \left [ log (B) + \frac{(x_t - \mu)^2}{B}\right ] \) .... where B and x_t are constants (for this instant)

Now differentiate above w.r.t. \(\displaystyle \mu\)

Please write back, with your work, for further help.