# Multivariate gaussian, MLE

#### Kiuhnm

##### New Member
How do you take the derivative of
$$\ln p(X|\mu,\Sigma)=-\frac{N D}{2}\ln(2\pi)-\frac{N}{2}\ln|\Sigma|-\frac{1}{2}\sum_{n=1}^N(x_n-\mu)^T\Sigma^{-1}(x_n-\mu)$$
with respect to $$\Sigma$$?

#### Kiuhnm

##### New Member
I'm really interested in what method you statisticians use when you have to deal with a novel expression (not something you can look up). Do you use matrix calculus? I'm aware of at least 3 approaches:
1) rewrite the expression in non-matrix form, compute the single partials and try to recompact the result into matrix form;
2) use Schonemann's method (paper);
3) use Magnus & Neudecker's method (book).
Just curious.