一道偏导数

  1. 8月前

    求详细过程

    • C8B7FF96-00FF-433F-A35B-D78B149B0CE2.jpeg
  2. 8月前zhrrr 重新编辑

    原方程为:
    $\Large F(x-z,y-z)=0$
    对x有:
    $\Large \frac{\partial F}{\partial u} (1-\frac{\partial z}{\partial x})+\frac{\partial F}{\partial v} (0-\frac{\partial z}{\partial x})=0 $
    即有:
    $ \Large \frac{\partial F}{\partial u} -\frac{\partial z}{\partial x}(\frac{\partial F}{\partial u}+\frac{\partial F}{\partial v})=0 \hspace{4cm} (1)$
    对y有:
    $\Large \frac{\partial F}{\partial u} (0-\frac{\partial z}{\partial y})+\frac{\partial F}{\partial v} (1-\frac{\partial z}{\partial y})=0 $
    即:
    $\Large \frac{\partial F}{\partial v} -\frac{\partial z}{\partial y}(\frac{\partial F}{\partial u}+\frac{\partial F}{\partial v})=0 \hspace{4cm} (2)$
    将上述两式相加有:
    $\Large \frac{\partial F}{\partial u}+\frac{\partial F}{\partial v}-(\frac{\partial z}{\partial x}+\frac{\partial z}{\partial y}) (\frac{\partial F}{\partial u}+\frac{\partial F}{\partial v})=0 $
    又因为
    $\Large \frac{\partial F}{\partial u}+\frac{\partial F}{\partial v} \neq 0$
    所以:
    $\Large \frac{\partial z}{\partial x}+\frac{\partial z}{\partial y}=1$

  3. 3月前

    感谢。。之前太忙没来得及回复。

 

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