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# è¯¾ é¢ ç¬¬ 4 ç« ãå¯¼æ°ä¸å¾®å 4.2 ãæ±å¯¼æ³åâ - PowerPoint PPT Presentation

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4.2　求导法则②

1．掌握隐函数求导法、对数求导法、参数方程求导法

2．掌握高阶导数的计算

4.2　求导法则②

(x ) = x-1 .

(ax) = ax lna .

(ex) = ex.

(sin x) = cos x.

(cos x) = - sin x.

(tan x)=sec2x .

(cot x)=- csc2x .

(csc x)=- csc x cot x .

(sec x)=sec x tan x .

1. 隐函数求导法

( xy )′= [ ln(x+ y) ]′

(1)在方程两边对 x 求导, 注意把 y 看成是 x 的函数;

(2)从方程中解出 y′.

3. 参数方程求导法

(a 为常数) 所确定的函数的导数 .

如对二阶导数再求导，则称三阶导数，

四阶或四阶以上导数记为 y(4)，y(5)，···，y(n)

f (x) 的一阶导数.

y  = ex，y = ex， ···，y(n) = ex .

y  = a0nxn-1+ a1(n-1)xn-2 + a2(n-2)xn-3 + … + an-1

y = a0n(n-1)xn-2+ a1(n-1) (n-2)xn-3

+ a2(n-2) (n-3)xn-4 + … + 2an-2