Fehr-Schmidt model and the Ultimatum Game [Economics]

Kolmin

I am perfectly aware that an answer to this question could take slightly more than the usual, but this thing is making me nut. I don’t get if I make some sort of mistake in terms of calculation or if the authors use a peculiar notation.

This is the paper that I am referring to, in particular page 826-828.

My problem is with s'(α₂)= α₂/(1+α₂).
It seems to me, this cannot be the first derivative of the proposal that has to be made as a function of the parameter α₂. Instead, it is simply the explicit version of s(α₂)= α₂/(1+α₂) [then, no derivative around...]

Do I miss something?

Thanks for your feedbacks.