Derivative of a matrix

[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 :)