求复合函数的一阶偏导数！(1)z=f(xy^2，x^2/y) (2)u=f（e^xy，y/x）5.
求复合函数的一阶偏导数！(1)z=f(xy^2，x^2/y)(2)u=f（e^xy，y/x）5.求du.u=f(xy,x/z)详情见图...
求复合函数的一阶偏导数！(1)z=f(xy^2，x^2/y)
(2)u=f（e^xy，y/x）5.求du. u=f(xy,x/z) 详情见图 展开
(2)u=f（e^xy，y/x）5.求du. u=f(xy,x/z) 详情见图 展开
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1）Z = f(xy^2，x^2/y)........Z = f(u，v).......u = xy².......v = x²/y
Z'x = (∂f/∂u)y² + 2(∂f/∂v)x/y
Z'y = 2(∂f/∂u)xy - (∂f/∂v)x²/y²
2) Z =f(e^xy，y/x).........Z = Z(u,v).......u=e^(xy).....v=y/x
Z'x = (∂f/∂u)e^(xy)y - (∂f/∂v)y/x²
Z'y = Z'y = (∂f/∂u)e^(xy)x - (∂f/∂v)/x
Z'x = (∂f/∂u)y² + 2(∂f/∂v)x/y
Z'y = 2(∂f/∂u)xy - (∂f/∂v)x²/y²
2) Z =f(e^xy，y/x).........Z = Z(u,v).......u=e^(xy).....v=y/x
Z'x = (∂f/∂u)e^(xy)y - (∂f/∂v)y/x²
Z'y = Z'y = (∂f/∂u)e^(xy)x - (∂f/∂v)/x
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