Is this an extinction rate, equilibrium constant, reaction constant or pH calculation arrived at during a chemical reaction equation? Just curious. I just dealt with those last semester.
I agree that the "prime" in "k' " is the notation used in ordinary differential calculus for the first derivative of a function k. It was confusing to me, too, when I came across it in a general chemistry class.
I think these calculations do involve derivatives and exponentiation at some point in the math happening "behind the scenes," because they are rates and deal with chemical reaction speeds and logarithmic values of ionic hydrogen concentrations in solutions. However, I think they are just alluding to it here or "telling you," without proving it mathematically. I asked similar questions and got "that's a different class, where you go over the derivation of these formulas."