I develop open-source statistical software (http://openmx.psyc.virginia.edu/), but matrix calculus is not my strong point. I need the 1st and 2nd derivatives of the log multivariate normal density. I was happy to find the 1st derivatives here on CrossValidated,

How to take derivative of multivariate normal density?

However, the 2nd derivatives are left as an exercise to the reader. I am sure the 2nd derivatives have been independently derived many times. However, I cannot find them exhibited anywhere. Is there a calculus expert out there who can detail the 2nd derivatives?

Many thanks.