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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