Differentiate log likelihood

morten23

New member
Joined
Jan 11, 2020
Messages
1
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).


Udklip.JPG

Thank you
 

Subhotosh Khan

Super Moderator
Staff member
Joined
Jun 18, 2007
Messages
22,163
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
1578760248996.png

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 xt are constants (for this instant)

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

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