>>615

u(x,y) = y/x とおけば

v=arctan(u)

なので

∂v/∂y
=(∂v/∂u)*(∂u/∂y)
=[1/(1+u^2)]*(1/x)
=[1/(1+(y/x)^2)]*(1/x)
=x/(x^2+y^2)

∂v/∂x
=(∂v/∂u)*(∂u/∂x)
=[1/(1+u^2)]*(-y/x^2)
=[1/(1+(y/x)^2)]*(-y/x^2)
=-y/(x^2+y^2)

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