we know that f(x) = 1 / (1 + e^(-2x)). find f'(x).


= (1 + e^(-2x))^-1

-1 * (1 + e^(-2x))^-2 * (0 + e^(-2x)*-2) :  power rule -> chain rule.

= 2 * e^(-2x) / (1 + e^(-2x))^2 : rewrite

-slim