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!