I want to study the derivability of this function
My textbook says the function is defined for $x>0$ (easy to understand for me, the argument of the logarithm must be positive) and it says: "it can certainly be derived for $x\neq 1$". I wonder how my textbook reached this conclusion without deriving the function first. I'm aware derivatives are defined like this:
Although I can't understand how we can reach conclusions about derivability just by looking at the function. Any hints?