求由方程xe^y+ye^x=0所确定的隐函数的导数dy/dx

xe^y+ye^x=0
直接对x求导
x' * e^y + x * (e^y)' + y' * e^x + y * (e^x)' = 0
e^y + x * e^y * y' + y' * e^x + y * e^x = 0
e^y + (x e^y + e^x)*y' + y e^x = 0
y' = - (e^y + ye^x)/(x e^y + e^x)
也可整理为
= - [e^(y-x) + y]/[x e^(y-x) +1)