116问答网 > 求复合函数的一阶偏导数！(1)z=f(xy^2，x^2⼀y) (2)u=f（e^xy，y⼀x）5.

求复合函数的一阶偏导数！(1)z=f(xy^2，x^2⼀y) (2)u=f（e^xy，y⼀x）5.

2024-11-19 01:48:36

推荐回答（2个）

回答1：

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

回答2：

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