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.
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