Derive an efficient method to compute the gradient of the log-likelihood function for the following mixture models: a. Gaussian mixture models: @ @ ln px,

Derive an efficient method to compute the gradient of the log-likelihood function for the following mixture models:

a. Gaussian mixture models: @

@ ln p¹xº, where p¹xº is given in Eq. (12.6).

b. Hidden Markov models: @

@ ln p¹oº, where p¹oº is given in Eq. (12.15).