what is the first derivative of the function u(S/(K+S)) = G(S) when u and K are constants?

Answer 1

so it appears that
g(s) = u * s/(k+s)
g'(s) = u * (1/(k+s) - s/(k+s)^2) = uk/(k+s)^2

Answer 2

Why would we not pull the k out as well? so u*1/k then just take the derivative of S over S? Is that because K+S are added in the denominator?

Answer 3

If you have to ask that question, you have forgotten your basic algebra.
plug in some numbers for u and k and see what you get.

If you want to go the long way around, use the quotient rule.