Matrix Derivative: Solving for \partial_{x}[\det(\textbf{1}-\textbf{M})]

[guerom00]

Hello

I scratch my head on trying to express \partial_{x}[\det(\textbf{1}-\textbf{M})] , where \textbf{M} is a square matrix whose elements depend on x, as an expression involving \textbf{M} and/or \partial_{x}\textbf{M}.
For instance, I have painfully noticed that it is not equal to \det(\textbf{1}-\partial_{x}\textbf{M})

Any help would be much apprciated TIA

 

[guerom00]

Nevermind…
This is the theorem I'm looking for exactly :)