函數(shù)的和、差、積、商的導(dǎo)數(shù)(8)課件

1、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(shí)回顧：知識(shí)回顧：)(0) 1 (為常數(shù)CC 練習(xí)：練習(xí)：1.1.求函數(shù)下列函數(shù)的導(dǎo)數(shù)求函數(shù)下列函數(shù)的導(dǎo)數(shù). .2(1) ( )f xx(2) ( )g xx2(3) ( )h xxx2.2.從以上計(jì)算結(jié)果從以上計(jì)算結(jié)果, ,你能發(fā)現(xiàn)什么你能發(fā)現(xiàn)什么? ? ( )( )( )( )f xg xfxg x兩個(gè)函數(shù)的和的導(dǎo)數(shù)兩個(gè)函數(shù)的和的導(dǎo)數(shù), ,等于這兩個(gè)

2、函數(shù)導(dǎo)數(shù)的和等于這兩個(gè)函數(shù)導(dǎo)數(shù)的和. .以上兩個(gè)函數(shù)的差的導(dǎo)數(shù)以上兩個(gè)函數(shù)的差的導(dǎo)數(shù), ,等于這兩個(gè)函數(shù)導(dǎo)數(shù)的差嗎？等于這兩個(gè)函數(shù)導(dǎo)數(shù)的差嗎？函數(shù)的函數(shù)的和、差、積、商和、差、積、商的導(dǎo)數(shù)的導(dǎo)數(shù)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(gè)函數(shù)的兩個(gè)函數(shù)的和（或差）的和（或差）的導(dǎo)數(shù)導(dǎo)數(shù)，等于這兩個(gè)函數(shù)的導(dǎo)數(shù)的和，等于這兩個(gè)函數(shù)的導(dǎo)數(shù)的和（或差），即：（

3、或差），即：).()( )()(xgxfxgxf法則法則2:2:).( )(為常數(shù)CxfCxCf說(shuō)明說(shuō)明: :求導(dǎo)法則的證明不作要求求導(dǎo)法則的證明不作要求. .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)xxxxg323223( )(62)23()()(6 )23362g xxxxxxxxx解：法則法則3:3:兩個(gè)函數(shù)的兩個(gè)函數(shù)的積的導(dǎo)數(shù)積的導(dǎo)數(shù)，等于，等于第一個(gè)函數(shù)的導(dǎo)數(shù)第一個(gè)函數(shù)的導(dǎo)數(shù)乘乘以第二個(gè)函數(shù)以第二個(gè)函數(shù), ,加加上第一個(gè)函數(shù)上第一個(gè)函數(shù)乘乘以第二個(gè)函數(shù)的導(dǎo)以第二個(gè)函數(shù)的導(dǎo)數(shù)數(shù)).

4、()()()( )()(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xxxfxxxhxxxxxxxxxxhcossin)(sinsin)sin()() 1 ( :解2ln2)(ln2(ln)2()ln2()()2(xxxxxxxxf 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. .3 32 298182xx解：解：) 23)(32 () 23 ( ) 32 (22xxxxy3)32()23(42 xxx法二：法二：法一：法一：)6946(23xxxy98182xx法則法則4 4 : :兩個(gè)函數(shù)的兩個(gè)函數(shù)的

5、商的導(dǎo)數(shù)商的導(dǎo)數(shù)，等于分，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其中的導(dǎo)數(shù)。）求函數(shù)（的導(dǎo)數(shù)求函數(shù)的導(dǎo)數(shù)求函數(shù)：例xxyxytttscos3tan)2(.1)()1(32的導(dǎo)數(shù).ex(4)求函數(shù)f(x)x的導(dǎo)數(shù).ex(4)求函數(shù)f(x)x22( )()()1()xxxxxxxxxfxex ex eexexeee課本課本P22 P22 練習(xí)練習(xí)函數(shù)的求導(dǎo)法則函數(shù)的求導(dǎo)法則: :(1) ( )( )( )( )f xg xf

6、xg x(2) ( )( )( )( )f xg xfxg x(3)( )( )()Cf xCfx C為常數(shù)(4) ( )( )( ) ( )( )( )f x g xfx g xf x g x2( )( ) ( )( )( )(5)( )( )f xfx g xf x g xg xgx1.1.求下列函數(shù)的導(dǎo)數(shù)求下列函數(shù)的導(dǎo)數(shù): :練習(xí)練習(xí):(1)(21)(32)yxx(2)sinyxxx(4)23xyx(1)(tan ).yx x21(3)xyexln(4)21xxyx2.2.求下列函數(shù)的導(dǎo)數(shù)求下列函數(shù)的導(dǎo)數(shù): :(3)22lnxyx(2)1 sincos22xxy 思考討論：思考討論：1.

7、(1)1.(1)已知函數(shù)已知函數(shù)f(x)的導(dǎo)數(shù)為的導(dǎo)數(shù)為 , ,則則 的導(dǎo)數(shù)的導(dǎo)數(shù) 為為 ,這句話對(duì)嗎這句話對(duì)嗎?( )f x2 ( )f x2( )f x (2) (2)已知函數(shù)已知函數(shù)f(x)的導(dǎo)數(shù)為的導(dǎo)數(shù)為 , ,則則函數(shù)函數(shù)f(x) .23x3x2.(1)2.(1)在曲線在曲線y=xy=x3 3+x-2+x-2上求一點(diǎn)上求一點(diǎn)P,P,使曲線在使曲線在P P處的切處的切線平行于直線線平行于直線4x-y-7=04x-y-7=0. . (2) (2)已知直線已知直線x-2y+4=0 x-2y+4=0和拋物線和拋物線x x2 2=4y=4y相交于相交于A,BA,B兩點(diǎn)兩點(diǎn), ,在弧在弧AOBAOB上求一點(diǎn)上求一點(diǎn)P,P,使使APBAPB的面積最大的面積最大, ,求求點(diǎn)點(diǎn)P P的坐標(biāo)的坐標(biāo). . (2) (2)已知直線已知直線x-2y+4=0 x-2y+4=0和