xy=e^(x+y)求dy/dx

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xy=e^(x+y)求dy/dx
xy=e^(x+y)求dy/dx

xy=e^(x+y)求dy/dx
xy=e^(x+y)求dy/dx 这是隐函数求导问题：正统方法是用：隐函数存在定理来做；另一方法是等式两边对x求导,再解出y'来：
方法1：f(x,y)=xy-e^(x+y)=0
dy/dx=-f'x/f'y
f'x=y-e^(x+y) f'y=x-e^(x+y)
dy/dx=-[y-e^(x+y)]/[x-e^(x+y)]
方法2：y+xy'=(1+y')e^(x+y)
xy'-y'e^(x+y)=e^(x+y)-y
解出：y'=[e^(x+y)-y]/[x-e^(x+y)]
两种方法结果是一样的.

dy/dx=(-y+e^(x+y))/(x-e^(x+y))

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