# Symbolic derivative in a sum

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uranus on 14 Mar 2024
Commented: David Goodmanson on 15 Mar 2024
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 ?

David Goodmanson on 14 Mar 2024
Edited: David Goodmanson on 14 Mar 2024
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 on 14 Mar 2024
Edited: uranus on 14 Mar 2024
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 on 15 Mar 2024
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..