求一道微积分的试题 设函数y=y(x)由方程e^xy+x+y=1确定,求dy/dx
问题描述:
求一道微积分的试题
设函数y=y(x)由方程e^xy+x+y=1确定,求dy/dx
答
对方程e^xy+x+y=1求导:
(e^xy)*y*dx+(e^xy)*xdy+dx+dy=0
dy/dx=-(y*e^xy+1)/(x*e^xy+1)