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導(dǎo)數(shù)的概念

一

1、當(dāng)函數(shù)在某一點(diǎn)a的導(dǎo)數(shù)無窮大，則在a點(diǎn)不可導(dǎo)

2、可導(dǎo)一定連續(xù)，連續(xù)不一定可導(dǎo)

導(dǎo)數(shù)存在和導(dǎo)數(shù)連續(xù)的區(qū)別：

①滿足條件不同

a、導(dǎo)數(shù)存在：只要存在左導(dǎo)數(shù)或者右導(dǎo)數(shù)就叫導(dǎo)數(shù)存在。

b、可導(dǎo)：左導(dǎo)數(shù)和右導(dǎo)數(shù)存在并且左導(dǎo)數(shù)和右導(dǎo)數(shù)相等才能叫可導(dǎo)。

②函數(shù)連續(xù)性不同

a、導(dǎo)數(shù)存在：導(dǎo)數(shù)存在的函數(shù)不一定連續(xù)。

b、可導(dǎo)：可導(dǎo)的函數(shù)一定連續(xù)；連續(xù)的函數(shù)不一定可導(dǎo)，不連續(xù)的函數(shù)一定不可導(dǎo)。

③曲線形狀不同

a、導(dǎo)數(shù)存在：曲線是不連續(xù)的，存在尖點(diǎn)或斷點(diǎn)。

b、可導(dǎo)：可導(dǎo)的曲線形狀是光滑的，連續(xù)的。沒有尖點(diǎn)、斷點(diǎn)。

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.

求導(dǎo)法則

二

1、求導(dǎo)公式

推導(dǎo) 例：

2、反函數(shù)求導(dǎo)

反函數(shù)求導(dǎo)=原函數(shù)導(dǎo)數(shù)的倒數(shù)

3、復(fù)合函數(shù)求導(dǎo)

①主要思路：由外向內(nèi)逐步求導(dǎo)

例：

補(bǔ)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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翻譯：谷歌翻譯
參考：《高等數(shù)學(xué)》第七版上冊 同濟(jì)大學(xué)數(shù)學(xué)系、百度
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