一、微分
概念
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-weifen-new-1.png" width="500" />
函数可微条件
- 如果函数可微，那么可导；
- 如果函数可导，那么可微；
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-weifen-new-2.png" width="500" />
求微分
- y=f(x) 的微分也就是函数 y＝f(x)的导数* dx , 所以求微分，也就是求导数；
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-weifen-new-3.png" width="500" />
凑微分，为积分做铺垫
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-weifen-new-4.png" width="500" />
二、微分中值定理
罗尔定理
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-weifen-new-5.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-weifen-new-6.png" width="500" />
拉格朗日中值定理 ( 很重要 )
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-weifen-new-7.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-weifen-new-8.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-weifen-new-9.png" width="500" />
洛必达法则
- 未定式, 0/0型和无穷/无穷型，０*无穷型和无穷－无穷型
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-weifen-new-10.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-weifen-new-11.png" width="500" />
- 0/0型 未定式的洛必达法则
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-weifen-new-12.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-weifen-new-13.png" width="500" />
- 无穷/无穷型 未定式的洛必达法则
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-weifen-new-14.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-weifen-new-15.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-weifen-new-16.png" width="500" />
- ０*无穷型和无穷－无穷型 未定式的洛必达法则可以转换为 0/0型 和 无穷/无穷型的未定式的洛必达法则
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-weifen-new-17.png" width="500" />
