方程ex+y次方-xy=0确定隐函数y=f(x),求dy/dx,求完整的答案,这是一道计算题,

Question

方程ex+y次方-xy=0确定隐函数y=f(x),求dy/dx,求完整的答案,这是一道计算题,

Answer 1

xy=e^(x+y)
两边对x求导,得：y+xy’=(1+y’)e^(x+y)
移项,得：[x-e^(x+y)]y’=e^(x+y)-y
整理得：y’=[e^(x+y)-y]/[x-e^(x+y)]
将xy=e^(x+y)代入,即把e^(x+y)换成xy,得：y’=(xy-y)/(x-xy)
所以dy/dx=(xy-y)/(x-xy)