Question

设y=y(x)是由方程ey+xy=1所确定的隐函数,求dy/dx

Answer 1

e^y + xy = 1 两边对x求导数：
y'e^y +y+xy'=0
y'(e^y +x)=-y
y'=dy/dx= -y/(e^y +x)
=-y/(1+x-xy)