y =ln0.5(1-e^(-x))
= ln(1-e^(-x)) + ln(0.5)
dy/dx = e^(-x)/(1-e^(-x) )
0.5e^(-y) -1
=0.5e^(-ln0.5(1-e^(-x) ) -1
= 1/(1-e^(-x)) -1
= e^(-x)/(1-e^(-x))
=dy/dx