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導數(shù)的概念
一
1、當函數(shù)在某一點a的導數(shù)無窮大，則在a點不可導
導數(shù)存在和導數(shù)連續(xù)的區(qū)別：
①滿足條件不同
a、導數(shù)存在：只要存在左導數(shù)或者右導數(shù)就叫導數(shù)存在。
b、可導：左導數(shù)和右導數(shù)存在并且左導數(shù)和右導數(shù)相等才能叫可導。
②函數(shù)連續(xù)性不同
a、導數(shù)存在：導數(shù)存在的函數(shù)不一定連續(xù)。
b、可導：可導的函數(shù)一定連續(xù)；連續(xù)的函數(shù)不一定可導，不連續(xù)的函數(shù)一定不可導。
③曲線形狀不同
a、導數(shù)存在：曲線是不連續(xù)的，存在尖點或斷點。
b、可導：可導的曲線形狀是光滑的，連續(xù)的。沒有尖點、斷點。
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.
求導法則
二
1、求導公式
推導 例：
2、反函數(shù)求導
反函數(shù)求導=原函數(shù)導數(shù)的倒數(shù)
3、復合函數(shù)求導
①主要思路：由外向內逐步求導
例：
補充：
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》第七版上冊 同濟大學數(shù)學系、百度
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