---
url: /notes/高等数学/一元函数微分学/index.md
---
## 导数的概念

![image-20220221172908471](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211729705.png)

![image-20220221172919210](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211729379.png)

## 导数的定义

![image-20220221172948912](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211729305.png)

![image-20220221173000842](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211730109.png)

## 导数的几何意义

![image-20220221173018315](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211730464.png)

## 函数可导性与连续性的关系

```
函数在某点连续是函数在该点可导的必要条件，但不是充分条件
```

## 函数的求导法则

![image-20220221173123277](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211731468.png)

![image-20220221173142998](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211731217.png)

![image-20220221173155864](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211731976.png)

![image-20220221173211400](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211732587.png)

![image-20220221173222029](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211732313.png)

![image-20220221173230939](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211732064.png)

## 高阶导数

![image-20220221173438185](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211734293.png)

![image-20220221173327592](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211733665.png)

![image-20220221173459157](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211734238.png)

## 隐函数及由参数方程所确定的函数的导数 相关变化率

![image-20220221173550537](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211735589.png)

![image-20220221173603267](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211736354.png)

![image-20220221173614935](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211736988.png)

## 函数的微分

![image-20220221173643153](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211736338.png)

![image-20220221173702590](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211737695.png)

![image-20220221173715955](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211737018.png)

![image-20220221173736824](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211737894.png)

![image-20220221173756247](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211737326.png)

## 微分中值定理

![image-20220221173825824](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211738934.png)

![image-20220221173844889](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211738039.png)

![image-20220221173904064](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211739164.png)

![image-20220221173919003](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211739089.png)

![image-20220221173933980](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211739104.png)

## 泰勒公式

![image-20220221174001345](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211740444.png)

![image-20220221174012753](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211740826.png)

## 洛必达法则

![image-20220221174031839](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211740980.png)

## 函数的单调性与曲线的凹凸性

![image-20220221174054612](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211740781.png)

![image-20220221174106935](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211741028.png)

## 函数的极值与最大最小值

![image-20220221174126540](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211741655.png)

![image-20220221174138349](https://note-1259190304.cos.ap-chengdu.myqcloud.com/note/202202211741397.png)