二元函数是空间中的曲面
一元函数是平面内的平面
一，概念及二元函数
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/mult_weifen/mult-function-1.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/mult_weifen/mult-function-2.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/mult_weifen/mult-function-3.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/mult_weifen/mult-function-4.png" width="500" />
二，二元函数偏导数
二元函数偏导数时，自变量每次只有一个变量变化
- x变，y不变
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/mult_weifen/mult-function-5.png" width="500" />
- y变，x不变
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/mult_weifen/mult-function-6.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/mult_weifen/mult-function-7.png" width="500" />
- 几元函数就有几个偏导数
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/mult_weifen/mult-function-8.png" width="500" />
三，偏导数计算
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/mult_weifen/mult-function-9.png" width="500" />
- 偏导数的记号是一个整体
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/mult_weifen/mult-function-10.png" width="500" />
- 偏导数特殊说明
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/mult_weifen/mult-function-11.png" width="500" />
四，全微分
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/mult_weifen/mult-function-12.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/mult_weifen/mult-function-13.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/mult_weifen/mult-function-14.png" width="500" />
五，二阶偏导数
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/mult_weifen/mult-function-15.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/mult_weifen/mult-function-16.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/mult_weifen/mult-function-17.png" width="500" />
六，多元复合函数求偏导
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/mult_weifen/mult-function-18.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/mult_weifen/mult-function-19.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/mult_weifen/mult-function-20.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/mult_weifen/mult-function-21.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/mult_weifen/mult-function-22.png" width="500" />
六，隐函数的导数和偏导数
显函数就是可以写为 y=x＋２, y=sinx.. 之类的形式;
隐函数就是非显函数的形式
二元方程就是一元函数的隐函数, 三元方程是二元函数的隐函数...
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/mult_weifen/mult-function-23.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/mult_weifen/mult-function-24.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/mult_weifen/mult-function-25.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/mult_weifen/mult-function-26.png" width="500" />
