2.1函數(shù)的和、差、積、商的導(dǎo)數(shù)蘇教版選修-ppt課件

1、3.2.2 3.2.2 函數(shù)的函數(shù)的和、差、積、商的導(dǎo)數(shù)和、差、積、商的導(dǎo)數(shù)為常數(shù)）(x)x)(2(11)a0,lna(aa)a)(3(xx且1)a, 0a (xlna1)xlog)(4(a且sinx(8)(cosx) e)e)(5(xxx1(6)(lnx) cosx )sinx)(7(基本求導(dǎo)公式基本求導(dǎo)公式: :知識回顧：知識回顧：)(0) 1 (為常數(shù)CC 2 2、由定義求導(dǎo)數(shù)三步法）、由定義求導(dǎo)數(shù)三步法）步驟步驟: :);()()1(xfxxfy 求增量求增量;)()()2(xxfxxfxy 算算比比值值常數(shù), 0)3(xyx當2)(xxfxxg)(4.4.結(jié)論：結(jié)論： . )()()

2、(22xxxx)()( )()(xgxfxgxf猜測：猜測：3 3利用導(dǎo)數(shù)定義求利用導(dǎo)數(shù)定義求 的導(dǎo)數(shù)的導(dǎo)數(shù). . xxy212)(2xxxxxxgxf2)()(證明猜想證明猜想).()()()(xgxfxgxf證明：令證明：令 ).()(xgxfy )()()()(xgxfxxgxxfy xxgxxgxfxxfxy)()()()( )()()()(xgxxgxfxxfxxgxxgxxfxxf)()()()()()(xgxf 法則法則1: 1: 兩個函數(shù)的和或差的兩個函數(shù)的和或差的導(dǎo)數(shù)，等于這兩個函數(shù)的導(dǎo)數(shù)的和導(dǎo)數(shù)，等于這兩個函數(shù)的導(dǎo)數(shù)的和或差），即：或差），即：).()( )()(xgxfx

3、gxf法則法則2:2:).( )(為常數(shù)CxfCxCf.sin)() 1 (. 12的導(dǎo)數(shù)求函數(shù)例xxxfxxxxxxxfcos2)(sin)()sin()(22解：.2623)()2(23的導(dǎo)數(shù)求函數(shù)xxxxg633)6()23()()623()(22323xxxxxxxxxg解：法則法則3:3:兩個函數(shù)的積的導(dǎo)數(shù)，等于兩個函數(shù)的積的導(dǎo)數(shù)，等于第一個函數(shù)的導(dǎo)數(shù)乘以第二個函數(shù)加第一個函數(shù)的導(dǎo)數(shù)乘以第二個函數(shù)加上第一個函數(shù)乘以第二個函數(shù)的導(dǎo)數(shù)上第一個函數(shù)乘以第二個函數(shù)的導(dǎo)數(shù)).()()()( )()(xgxfxgxfxgxf.ln2)()2(.sin)() 1 (2的導(dǎo)數(shù)求函數(shù)的導(dǎo)數(shù)求函數(shù)：例x

4、xxfxxxhxxxxxxxxxxhcossin)(sinsin)sin()() 1 ( :解2ln2)(ln2(ln)2()ln2()()2(xxxxxxxxf法則法則4 :4 :兩個函數(shù)的商的導(dǎo)數(shù)，等于分兩個函數(shù)的商的導(dǎo)數(shù)，等于分子的導(dǎo)數(shù)與分母的積，減去分母的導(dǎo)數(shù)子的導(dǎo)數(shù)與分母的積，減去分母的導(dǎo)數(shù)與分子的積，再除以分母的平方與分子的積，再除以分母的平方, ,即：即： )()()()()()()(2xgxgxfxgxfxgxf0)(xg其中.1)() 1 (32的導(dǎo)數(shù)求函數(shù)：例ttts222222222112) 1() 1()1()() 1 ( :解ttttttttttttts的導(dǎo)數(shù).ex(

5、2)求函數(shù)f(x)xxxxxxxxxexexeeeexexexxf1)()()()()2( :解22的導(dǎo)數(shù)的導(dǎo)數(shù)4 45x5x3x3x2x2xy y求求1.1.2 23 3練練 習習566)4532(:解223xxxxxy的導(dǎo)數(shù)的導(dǎo)數(shù)2)2)3)(3x3)(3x(2x(2xy y用兩種方法求用兩種方法求2.2.2 298182xx解：解：) 23)(32 () 23 ( ) 32 (22xxxxy3)32()23(42 xxx法二：法二：法一：法一：)6946(23xxxy98182xx的導(dǎo)數(shù)的導(dǎo)數(shù)xxysin. 32 xxxxxy222sin)(sinsin)(解：xxxxx22sincossin2處處的的導(dǎo)導(dǎo)數(shù)數(shù)在在點點求求333. 42 xxxy222) 3(2) 3() 3(1xxxxy解：222) 3(36xxx61)33(3363)3(,3222fx時當例例4:4:求曲線求曲線y=x3+3xy=x3+3x8 8在在x=2x=2處的切線的方程處的切線的方程. .02415),2(156:),6 , 2(15323)2(33)83()(:223yxxyfxxxxf即切線方