what is the derivative G(s) = s^2/(k^2+s^2)?
(k^2+s^2)(2s)-s^2(2K+2S)/(K^2+S^2)^2 is this correct?
not even close. k is a constant, so d/ds (k^2+s^2) is just 2s
Now.
s^2/(k^2+s^2) = 1 - k^2/(k^2+s^2) = -k^2 (k^s+s^2)^-1
so, the derivative is 2sk^2 (k^2+s^2)^-2
If you want to use the quotient rule, then that would be
(2s(k^2+s^2) - s^2(2s))/(k^2+s^2)^2
= (2sk^2+2s^3 - 2s^3)/(k^2+s^2)^2
= 2sk^2/(k^2+s^2)^2