已知xy-e^y=0,求d^2y/dx^2

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已知xy-e^y=0,求d^2y/dx^2

xy-e^y=0
y+xdy/dx-e^y·dy/dx=0
dy/dx=y/(e^y-x)
d²y/dx²=[dy/dx·(e^y-x)-y(e^y·dy/dx-1)]/(e^y-x)²
把dy/dx=y/(e^y-x)代入上式得
d²y/dx²=[y-y²e^y/(e^y-x)]/(e^y-x)²