Derivative of multivariate normal distribution wrt mean and covariance I want to differentiate this wrt $\mu$ and $\Sigma$ :
$${1\over \sqrt{(2\pi)^k |\Sigma |}} e^{-0.5 (x-\mu)^T \Sigma^{-1} (x-\mu)} $$  
I'm following the matrix cookbook here and also this answer . The solution given in the answer (2nd link), doesn't match with what I read in the cookbook.
For example, for this term, if I follow rule 81 from the linked cookbook, I get a different answer (differentiating wrt $\mu$) :
$(x-\mu)^T \Sigma^{-1} (x-\mu)$  
According to the cookbook, the answer should be : $-(\Sigma^{-1} + \Sigma^{-T}) (x-\mu)$ . Or, am I missing something here? Also, how do I differentiate $(x-\mu)^T \Sigma^{-1} (x-\mu)$
 with respect to $\Sigma$ ?

If you're trying to find the derivative with respect to $\mu\in\mathbb R^{n\times 1}$ and $\Sigma\in\mathbb R^{n\times n}$, then I don't think the answer could possibly be $(\Sigma^{-1} + \Sigma^{-T}) (x-\mu)$.  I'm wondering if what you're trying to do is find the values of $\mu$ and $\Sigma$ that maximize the expression you wrote, then perhaps This section from Wikipedia will shed some light.
