Question

函数……问题求过程，大佬帮帮忙

Answer 1

商的导数十复合函数求导：
y=xe^y
y'=e^y+xe^y.y'
y'(1-xe^y)=e^y
y'=e^y/(1-xe^y)
y''=[e^y.y'(1-xe^y)-e^y(-e^y-xe^y.y')]/(1-xe^y)²
=[e^y.y'(1-xe^y)+e^y(e^y+xe^y.y')]/(1-xe^y)²
=[e^y.y'-xe^2y.y'+e^2y+xe^2y.y']/(1-xe^y)²
=[e^y.y'+e^2y]/(1-xe^y)²
=e^y(y'+e^y)/(1-xe^y)²
=e^y(e^y/(1-xe^y)+e^y)/(1-xe^y)²
=e^2y(1/(1-xe^y)+1)/(1-xe^y)²
=e^2y(2-xe^y)/(1-xe^y)³
y=xe^y代入：
y''=e^2y(2-y)/(1-y)³
y'=e^y/(1-y)