e^xy+x+y=2求dy/dx |x=1

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e^xy+x+y=2求dy/dx |x=1
e^xy+x+y=2求dy/dx |x=1

e^xy+x+y=2求dy/dx |x=1
f(x,y)=e^xy+x+y=2
求全微分 (Df/Dx)dx+(Df/Dy)dy=0
dy/dx=-(y*e^xy+1)/(x*e^xy+1)
如果 x=1
dy/dx |x=1 = -(ye^y+1)/(e^y+1)
其中y为 f(1,y)=2 的解,即y满足 e^y+1+y=2=>e^y+y=1 => y=0 （这是特殊情况,一般此类方程没有显式的解）
所以
dy/dx |x=1 = -1/2

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