matrices – Does $frac{partial}{partialepsilon}(hat A+hat{O}cdotepsilon) = hat{O}$?

I’m wondering does $frac{partial}{partialepsilon}(hat A+hat{O}cdotepsilon) = hat{O}$ ? Here, $hat A$ and $hat{O}$ refer to some operators which could be represented as matrices. I think that’s true from intuition, but I’m not sure if I could just treat those operators as some variables like $x$ and $y$. Thanks for the help!