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.