已知z=arctany/x求az/ax,az/ay

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已知z=arctany/x求az/ax,az/ay已知z=arctany/x求az/ax,az/ay已知z=arctany/x求az/ax,az/ay∂z/∂x=1/(1+y^

已知z=arctany/x求az/ax,az/ay
已知z=arctany/x求az/ax,az/ay

已知z=arctany/x求az/ax,az/ay
∂z/∂x
=1/(1+y^2/x^2)*(y/x)'
=x^2/(x^2+y^2)*y*(-1/x^2)
=-y/(x^2+y^2)
∂z/∂y
=1/(1+y^2/x^2)*(y/x)'
=x^2/(x^2+y^2)*(1/x)
=x/(x^2+y^2)