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两边取对数：
½ln(x²+y²)=arctan(y/x)
两过求导
½[(2x+2yy′)/(x²+y²)=[(xy′-y)/x²)/[1+(y/x)²]
(x+yy′)/(x²+y²)=(xy′-y)/(x²+y²)
x+yy′=xy′-y
(x-y)y′=x+y
y′=(x+y)/(x-y)
y′′=[(1+y′)(x-y)-(x+y)(1-y′)]/(x-y)²
将y′代入上式
y′′=[(1+(x+y)/(x-y))(x-y)-(x+y)(1-(x+y)/(x-y))]/(x-y)²
y′′=2(x²+y²)/(x-y)³
½ln(x²+y²)=arctan(y/x)
两过求导
½[(2x+2yy′)/(x²+y²)=[(xy′-y)/x²)/[1+(y/x)²]
(x+yy′)/(x²+y²)=(xy′-y)/(x²+y²)
x+yy′=xy′-y
(x-y)y′=x+y
y′=(x+y)/(x-y)
y′′=[(1+y′)(x-y)-(x+y)(1-y′)]/(x-y)²
将y′代入上式
y′′=[(1+(x+y)/(x-y))(x-y)-(x+y)(1-(x+y)/(x-y))]/(x-y)²
y′′=2(x²+y²)/(x-y)³
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