# 一道偏导数

1. 8月前

1楼 2018年6月1日

求详细过程

2. ### zhrrr

2楼 2018年6月4日
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

### 嘉二爷

3楼 10月27日

感谢。。之前太忙没来得及回复。