请问这道微积分怎么解决，第八道
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ln√(x^2+y^2) = arctan(y/x)
(1/2)ln(x^2+y^2) = arctan(y/x)
两边求导
(x + y.dy/dx)/(x^2+y^2) ={ 1/[ 1+(y/x)^2] } . [ (x.dy/dx - y )/x^2 ]
= (x.dy/dx - y )/(x^2+y^2)
x+ y.dy/dx = x.dy/dx - y
(x-y).dy/dx = x+y
dy/dx = (x+y)/(x-y)
ln√(x^2+y^2) = arctan(y/x)
(1/2)ln(x^2+y^2) = arctan(y/x)
两边求导
(x + y.dy/dx)/(x^2+y^2) ={ 1/[ 1+(y/x)^2] } . [ (x.dy/dx - y )/x^2 ]
= (x.dy/dx - y )/(x^2+y^2)
x+ y.dy/dx = x.dy/dx - y
(x-y).dy/dx = x+y
dy/dx = (x+y)/(x-y)
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