Question

y=x(e^y)的二次求导?

Answer 1

y=xe^y

y'=e^y+xe^y*y'

所以：

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(e^y-y')/(1-xe^y)^2

=-xe^3y/(1-xe^y)^2.