Symbolic derivative in a sum

I have this expression and I want to evaluate the derivative over p where A_m has a form like that:

It don't know even where to start from. Is there any way to do it ?

Answer 1

[David Goodmanson]

Hello OG,

If you know d/dp G for the elements of G, you can use

d/dp G^-1 = -G^-1 (d/dp G) G^-1

which is all right numerically, But if you want to do the whole thing symbolically, unless the size of G is really small this will turn into a huge intractable mess of symbolic spaghetti very quickly.

[uranus]

I have already tried that, but then it turns into (also a mess of) normal differentiation, but I can write it explicitly. Thus, is it not anymore symbolic, right? The system is of the order of 20 but I think this is sufficient to get the spaghetti!

[David Goodmanson]

If you know (d/dp G) either symbolically or numerically then you can get it numerically, and after that it would appear that numerical evaluation of the expression -G^-1 (d/dp G) G^-1 for a 20x20 should work reasonably well, unless G is close to being singular and has a bad condition number..