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

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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).

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