x*e的y次方-y+e=0的二阶导数

2025-06-20 15:01:34
推荐回答(1个)
回答1:

x*e^y-y+e=0
对x求导,可知
e^y+xe^y*y'-y'+0=0
则y'=e^y/(1-xe^y)
再求二阶导可知
y''=[e^y/(1-xe^y)]'
=[e^y*y'(1-xe^y)+e^y(e^y+xe^y*y')]/(1-xe^y)]^2
=[e^(2y)+e^(2y)*(1+xe^y/(1-xe^y)]/(1-xe^y)]^2
=[2e^(2y)-xe^(3y)]/(1-xe^y)]^3