Differentiate the logarithmic series to obtain a logistic expansion

Given $y=\ln(1+e^x)$, show $y^{\prime\prime}=y^{\prime}-(y^{\prime})^2$.3 marks

Hence find its Maclaurin series through $x^2$.2 marks

Deduce the first two nonzero terms in the expansion of $e^x/(1+e^x)$.3 marks