So looking through my notes I cant seem to understand how to get from one step to the next. I have attached a screenshot of the 2 lines I'm very confused about. Thanks.(adsbygoogle = window.adsbygoogle || []).push({});

BTW: The equations are for the log likelihood in a mixture of gaussians model

EDIT: To elaborate I am particularly confused about how they get numerator term π_{k} N(x_{n}|μ_{k}, Σ). I can't seem to understand how they are differentiating this to obtain that. I understand how they obtain the denominator term from differentiating the log but thats about all. To differentiate the multivariate gaussian I would think the log function needs to be used to break up the internal terms. Although I cant put this intuition together.

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# Derivative of Log Likelihood Function

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