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ln√(x^2+y^2) = arctan(y/x)
令 F(x, y) = ln√(x^2+y^2) - arctan(y/x) = (1/2)ln(x^2+y^2) - arctan(y/x)
则 ∂F/∂x = x/(x^2+y^2) - (-y/x^2)/[1+(y/x)^2] = (x+y)/(x^2+y^2)
∂F/∂y = y/(x^2+y^2) - (1/x)/[1+(y/x)^2] = (y-x)/(x^2+y^2)
得 ∂y/∂x = - (∂F/∂x)/(∂F/∂y) = (x+y)/(x-y)
令 F(x, y) = ln√(x^2+y^2) - arctan(y/x) = (1/2)ln(x^2+y^2) - arctan(y/x)
则 ∂F/∂x = x/(x^2+y^2) - (-y/x^2)/[1+(y/x)^2] = (x+y)/(x^2+y^2)
∂F/∂y = y/(x^2+y^2) - (1/x)/[1+(y/x)^2] = (y-x)/(x^2+y^2)
得 ∂y/∂x = - (∂F/∂x)/(∂F/∂y) = (x+y)/(x-y)
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