高数三大求导方法（好学高数三）

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导数的概念

一

1、当函数在某一点a的导数无穷大，则在a点不可导

2、可导一定连续，连续不一定可导

导数存在和导数连续的区别：

①满足条件不同

a、导数存在：只要存在左导数或者右导数就叫导数存在。

b、可导：左导数和右导数存在并且左导数和右导数相等才能叫可导。

②函数连续性不同

a、导数存在：导数存在的函数不一定连续。

b、可导：可导的函数一定连续；连续的函数不一定可导，不连续的函数一定不可导。

③曲线形状不同

a、导数存在：曲线是不连续的，存在尖点或断点。

b、可导：可导的曲线形状是光滑的，连续的。没有尖点、断点。

First, the derivative concept

1, when the derivative of the function at a point is infinite, it is not derivable at point a

2, derivable must be continuous, and the difference between the continuous and the derivative is not necessarily derivable:

1) the conditions are different

a, the derivative exists: as long as there is a left derivative or a right derivative, it is called the derivative existence. b. Derivable: The existence of the left and right derivatives and the equality of the left and right derivatives can be called derivable.

2) The function continuity is different

a、the derivative exists: the function in which the derivative exists is not necessarily continuous.

b. Derivable: the derivable function must be continuous; Continuous functions are not necessarily derivable, and discontinuous functions must not be derivable.

(3) The shape of the curve is different

a, the derivative exists: the curve is discontinuous, and there are sharp points or breakpoints.

b, conductive: the shape of the conductive curve is smooth and continuous. There are no sharp points, breakpoints.

求导法则

二

1、求导公式

推导 例：

2、反函数求导

反函数求导=原函数导数的倒数

3、复合函数求导

①主要思路：由外向内逐步求导

例：

补充：

Second, the law of differentiation

1, the derivative formula

2, the inverse function to derive the inverse function derivative = the reciprocal of the original function derivative

3, composite function derivation

(1) The main idea: from the outside to the inner step by step derivation

END

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翻译：谷歌翻译参考：《高等数学》第七版上册 同济大学数学系、百度声明：本文有LearningYard新学苑原创，若有侵权请联系删除

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