求达人解高数习题设y=f(x)是方程xy-e^x+e^y=0确定的隐函数,求dy/dx

求达人解高数习题设y=f(x)是方程xy-e^x+e^y=0确定的隐函数,求dy/dx
求达人解高数习题
设y=f(x)是方程xy-e^x+e^y=0确定的隐函数,求dy/dx

求达人解高数习题设y=f(x)是方程xy-e^x+e^y=0确定的隐函数,求dy/dx
xy-e^x+e^y=0
方程两边同时对x求导:
(x)′·y+x·(y)′-e^x+e^y·y′=0
∴y+x·dy/dx-e^x+e^y·dy/dx=0
∴dy/dx=(e^x-y)/(x+e^y)