y=ln0.5(1- e^-x)证明dy/dx = 0.5e^-y - 1
问题描述：
y=ln0.5(1- e^-x)
证明dy/dx = 0.5e^-y - 1
答
e^y = 0.5[1-e^(-x)]
de^y/dx = e^ydy/dx = 0.5e^(-x)
似乎不可能等于你那个式子
答
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