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导数的基本运算.

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Presentation on theme: "导数的基本运算."— Presentation transcript:

1 导数的基本运算

2 一、基本导数公式 1 ) (arctan (arcsin ln (log ( sec (sec (tan cos (sin x a
2 1 ) (arctan (arcsin ln (log ( sec (sec (tan cos (sin x a xtanx C + = - 2 1 ) cot ( (arccos (ln csc (csc (cot sin (cos x e xcotx + - = m

3 例1 求下列函数的导数:

4 二、求导法则 (1) 函数的和、差、积、商的求导法则

5   例 2 设 f (x) = 3x4 – ex + 5cos x - 1,求 f (x) 及 f (0). 
解  f (x) = (3x4 - ex + 5cos x - 1)  = (3x4)  -(ex ) + (5cos x)  - (1) = 12x3 - ex - 5sin x . f (0) = (12x3 - ex - 5sin x)|x=0 = - 1

6 例 3 设 y = xlnx , 求 y . 解 根据乘法公式,有 y = (xlnx) = x (lnx) + (x)lnx

7 例 4 设 求 y . 解 根据除法公式,有

8 二、求导法则 (2) 复合函数的求导法则 法则说明:复合函数对自变量的导数等于复合函数对中间变量的导数乘以中间变量对自变量的导数.

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