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Share interests, spread happiness, grow insights, and leave a good life! Dear you, this is the new Academy of LearningYard. Today Xiaobian brings you the good learning of high numbers (3): the law of differentiation of functions
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
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