zl1883com:函数的和、差、积、商的导数二_图文

zdg10989435 www.16954.com 666zzz.com www.69paopao.com WWW.77000.COM www.80299.com qifa758.com

qifa54 www.152ee.com www.2c402.com www.992208.com 900686 www.jnh33.com www.ptbet4.com

知识回顾:

基本求导公式:

(1)C? ? 0(C为常数)
(?为常数)

(2)( x ) ? ?x
x ' x
'

? '

? ?1

(3)(a ) ? a lna(a ? 0, 且a ? 1)
1 (4)(log a x ) ? (a ? 0, 且a ? 1) xlna 1 ' x ' x (6)(lnx) ? (5)(e ) ? e x

(7)(sinx ) ? cosx
'

(8)(cosx) ? ?sinx
'

练习:
1.求函数下列函数的导数.

(1) f ( x) ? x

2

(2) g ( x) ? x

(3)h( x) ? x ? x
2

2.从以上计算结果,你能发现什么?

[ f ( x) ? g ( x)] ? f ( x) ? g ( x)
' ' '

两个函数的和的导数,等于这两个函数导数的和. 以上两个函数的差的导数,等于这两个函数导数的差吗?

函数的和、差、积、商 的导数

证明猜想
证明:令

? f ( x) ? g ( x)?
y ? f ( x) ? g ( x).

?

? f ?( x) ? g ?( x).

?y ? ? f ( x ? ?x) ? g ( x ? ?x)?? ? f ( x) ? g ( x)?

? ? f ( x ? ?x) ? f ( x)? ? ?g ( x ? ?x) ? g ( x)?
?y ? f ( x ? ?x) ? f ( x)? ? ?g ( x ? ?x) ? g ( x)? ? ? ?x ?x

? f ( x ? ?x) ? f ( x)? ?g ( x ? ?x) ? g ( x)? ? ?
?x ?x

? f ?( x) ? g ?( x)

法则1: 两个函数的和(或差)的 导数,等于这两个函数的导数的和 (或差),即:

[ f ( x) ? g ( x)]? ? f ?( x) ? g ?( x).
法则2:

[Cf ( x)]? ? Cf ?( x).(C为常数)
说明:求导法则的证明不作要求.

例1. (1)求函数f ( x) ? x ? sin x的导数.
2

解:f ?( x) ? ( x ? sin x)?
2

? ( x )? ? (sin x)? ? 2 x ? cos x
2

3 2 (2)求函数g ( x) ? x ? x ? 6 x ? 2的导数. 2
3

3 2 解:g ?( x) ? ( x ? x ? 6 x ? 2)? 2 3 2 3 ? ( x )? ? ( x )? ? (6 x)? ? 2' ? 3 x 2 ? 3 x ? 6 2
3

法则 3: 两个函数的积的导数,等于

第一个函数的导数乘以第二个函数 ,
加上第一个函数乘以第二个函数的导 数

[ f ( x) g ( x)]? ? f ?( x) g ( x) ? f ( x) g ?( x).

例2: (1)求函数h( x) ? x sin x的导数. (2)求函数f ( x) ? 2 x ln x的导数.
解 : (1)h?( x) ? ( x sin x)? ? x? sin x ? x(sin x)? ? sin x ? x cos x

(2) f ?( x) ? (2 x ln x)? ? (2 x)? ln x ? (2 x)(ln x)? ? 2 ln x ? 2

?3?.用两种方法求y ?(2x
的导数

2

? 3)(3x? 2)

2 2 解: 法一:y? ? (2x ? 3)?(3x ? 2) ? (2x ? 3)(3x ? 2)?

? 4 x ( 3 x ? 2) ? ( 2 x ? 3) ? 3
2

? 18 x ? 8 x ? 9 3 2 法二: y? ? (6 x ? 4 x ? 9 x ? 6)?
2

? 18 x ? 8 x ? 9
2

法则4 :两个函数的商的导数,等于分

子的导数与分母的积,减去分母的导数 与分子的积,再除以分母的平方,即:

f ( x) f ?( x) g ( x) ? f ( x) g ?( x) [ ]? ? 2 g ( x) g ( x)

其中g ( x) ? 0

t ?1 例3: (1)求函数s (t ) ? t 的导数.
2

( 2)求函数y ? t an x的导数

x (4)求函数f(x) ? x 的导数. e

cos x (3 )求函数y ? 的导数 x

x (4)求函数f(x) ? x 的导数. e x
e x x x x x?e ? x(e )? e ? xe 1 ? x ? ? ? x 2 2x x (e ) e e
课本P22 练习

f ?( x) ? (

? ) x

函数的求导法则:
(1)[ f ( x) ? g ( x)] ? f ( x) ? g ( x)
' ' '

(2)[ f ( x) ? g ( x)]' ? f ' ( x) ? g ' ( x) (3)[Cf ( x)]' ? Cf ' ( x)(C为常数) (4)[ f ( x) g ( x)]' ? f ' ( x) g ( x) ? f ( x) g ' ( x)
f ( x) ' f ( x) g ( x) ? f ( x) g ( x) (5)[ ]? 2 g ( x) g ( x)
' '

练习:
1.求下列函数的导数:
(1) y ? (2 x ?1)(3x ? 2)
x x (2) y ? 1 ? sin cos 2 2 x (4) y ? 2x ? 3

(3) y ? 2x ? 2ln x
2.求下列函数的导数:
(1) y ? (tan x).x
1 (3) y ? e ? 2 x
?x

(2) y ? x sin x ? x ln x (4) y ? ? 2x x ?1

思考讨论:
1.(1)已知函数f(x)的导数为 f ' ( x),则[ f ( x)]2 的导数 为 2 f ' ( x) ,这句话对吗? (2)已知函数f(x)的导数为 3 x 2 ,则函数f(x) ? x3 . 2.(1)在曲线y=x3+x-2上求一点P,使曲线在P处的切 线平行于直线4x-y-7=0. (2)已知直线x-2y+4=0和抛物线x2=4y相交于A,B 两点,在弧AOB上求一点P,使△APB的面积最大,求 点P的坐标.

(2)已知直线x-2y+4=0和抛物线x2=4y相交于A,B 两点,在弧AOB上求一点P,使△APB的面积最大,求 点P的坐标.
y
B

A

P

O

x


以下是今天幸运会员获奖名单

wapwyt.com,187866.cc,www.146342.com,qyy4560com,wwW、huangpiang,wwwk310com,www.ycxbx.com,7272df,baijinhuiyulechang,dw9969,js2946com,WWW.BET039.COM

www.614123.com,www.sb6601.com,11622jm.com,2323721686@qq.com,www.34nl.com,3001155.com,lrdst888,www9168com,js75.com,www.494477.com,uhyv8,sun898.com,www.vip.hg02088.com,99rerezheliyoujingpinshouye,www745515com,www.2078e.com,www803195cn,www.j6030.com,www533933com,www.casio888.com,tcp099.com,22296ai.com,www.282833d.com,9ag88.com,91365365com,hkgolden.com,www.haohao66.com,www993996com,www.hg6675.net,WWW.5023.COM,4590010.com,qyy3944com,susu9506354,laoguan258,www.625410.com,29262540@QQ.COM,841111.com,www.hbnews.net,qingchenghuoshuizhendeyaofeishuigandongtxtxiazai,www.lhj6780.com,www.hg4596.com,www411039com,www.yibodo.com,ub66.net,ks5745com,wwwbai9966com,www.250pp.com,yibendaogaoqingshipinbukadvd,js4199com,yb7201vip,xinshijiguoji,hg00157.vip,www99135vcom,blh5522com,50fhyl,xpj9017.com,在线香蕉网络电视tv免费频道,6w22.com,4372i.com,WWW.678TK.COM,55dydy.com,www.cpcpcp888.com,www027com,www.j669.net,ttt844.com,www.068605.com,久章草在线视频免费观看,www1231777com,www.140361.com,wwwrb095com,944660.com,8639.com,www.hycai.com,3650088.com,www.tlc8829.com,861632com,www.906tv.com,www.c08282.com,wwwpb0111com,www98778com,whb78,http://ffnn.live/index.php?,wenchao1,xiaocai521,wwwbog5678com,876355258@qq.com,811882com,api.hooos.com,aiqianmei,www.hk6688.com,www.hg2228.net,888253com,www3848com,jbl8801.com,www1952com,japanesevisazaixian,329ks.net,817964com,WWW.W110011.COM,377nnn. com,www.5252c.com,www.hg25880.com,vi95662l,WWW.99195.COM,wp598.com,www3158cncc,www.eee141.net,www.88066.com,1976.com,3650009.com,www.js017.com,1025988277@qq.com,WWW.HJ886.COM,hg00515.cc,www.hg407.net,www888233com,www7773com,8946.com,bet365738365,www.ble01355.com,yb8615com,676298,aqd. xyz,www.wap365365.com,wwwjb587com,www084321com,www.898v.com,www1933com,www.bs79.com,yuren66.com,www.6161.com.cn,sinnistar.com,13644197070,li168,第四色男人最爱的网站,da335com,kb7351com,www.tt124.com,rt-motorcom,yanzcoli,www.1307cc.com,www.5559499.com,349816630,av5516. com,mitao520.com,7yyhh,66law.cn,www.mg6552.com,13809800403@qq.com,www.37419.com,www.ppcao222.com,0235ss.com,www.1302pp.com,www37288com,www.cddwt.net,www426000com,68519.com,wwwhg9690com,www.8302.com,www.20327.com,850321com,ilu99,chenbao123,www.199389.com,qifa54,wwwp6606com,hzk0088,www.06sihu.com|

d9002com,vns9134com,9567js.com,www.hg4252.com,857878.com,www.7733f.com,231se.com,www.1122sps.xom,www.131qq.com,czxf2002115,www.blm777777.com,www26suncitycom,www.79956.com,377381536,wan1328.com,www.youfa223.com,tyc5763.com,www.9mine.com,www.dfe2.com,jbl8980.com,pj0077.com,445544.net,jzplay8.com,www.777tb.com,www.gay6633 http://m.,amingli,www.ppp,150mm,www.88188n.cc,wwwpjzx22com,asd2580,www.123afghan.com,hg3336com,2672.com,xuebaolaohujichudaguiguilü,829645com,WWW.8182.COM,asd4567,m.hy241.com,www.87000.com,xl882,www035929com,800236com,www.yonghaoqp.com,1101792394,xpj2838com,www.mzdc7.com,wangfeng0913,88455,ag4761cn,www.570aa.com,www.44442q.com,WWW.OK556677.COM,www658968com,wwwhaole002com,zbnzbn595,wwwceo2008com,www50fafacom,WWW3838LUMM3COM_WWW.3838LUMM3,COM,3288989,258733453@qq.com,www.77518.loan,www.ztshipping.com,www.41668q.com,wwwzunbao140com,xalhar.mtv,www.tk,aomenyinhe111cc,www.cp77aa.com,ag84911,www.618410.com,www.895.com,一路向西观看118分钟,wwwbet66222com,www.585878.cc,WWW.CB577.NET,www.328789.com,ag7064999com,cytsyts,www84818com,www.hg5318.com,kaipitineishijieliuxiaoshuo,fh6619,www.awrig.cn,www.9087.net,www.23400.com,wwws333cpcom,www.919zy.com,nanndewo,www2146mcom,gao008.com,672ksnet,www.js6522.com,gl205,www282288com,48516.com,ks2943.vip,wwwhg2929biz,4691.bet,www.x7571.com,68809f.com,www.898788.com,www.3940.com,3041111com,www260222com,yh8213com,www.youfa287.com,www8889com,www.77xxaa.com,fengliang,91800m,11909com,3559ddd.com,qifa501.com,www.yabo.com,wwwjs999345co,z88333.com,www.jh29.com,www.2229v.com,21ruru.com,158867635@qq.com,sankakucomplex,www780iicom,18a62v千部爱库,www.tb0555.com,yx303831404,www531065295com,youjizz在线观看,bai0005,wwwc265555com,hg6482com,df99com,eejcl.con,916lao.com,www.pj89888.com,www.92dudu.com,rb228.com,www.am6691.com,www.miya177.com,www.111430.com,tiehan,2819453751@qq.com,syf1230,833798com,zva668,359592366@qq.com,yundingyuleanzhuoban,563270609,ku418.com,www.kkkk4438.com,www.6988.com,wan4438.com,365toya01,5f22.com,WWW.HJC777.COM,lh5344.com,www.shichang.com,wwwn89.cn,www.111com,www2967com,wwwin777com,ab1512.com,www44488vcom,www.7k.com,www.1ppkk.com,xpj4831.com,ag118.net,www.72vpvp.com|

WWW.0029.CC,www871630com,www.125065.com,422181315,www.9933033.com,WWW.88MSC.BIZ,h29h com,www940msccom,yh4706.com,www.153099.com,5829.win,quanluotiwuzhelanmeiren,ll1920,www40898300com,987000..com,5566lu,www18933oocom,zjhzjh1,WWWYAHOO_WWW.YAHOO,70900,www.2979o.com,4838.com,ag80908fcom,www.5556795.com,ugib7f,www.444fn.com,wcd1990,www.kkxxee.cow,497970.com,www.1721.com,lh8491.com,www.laowailu.com,hhmh11.com hhmh12.com ....,www.yh4971.com,www.www.buyu705.com,www.207365.com,616.net,WWW.P35DD.COM,wwwmg9412com,WWW.LIBO866.NET,www.61124.com,qqcgood,175856987,czy3746509,yth94.net,xpj2568.com,wwwgs51888com,535cssts,tangweiheliangchaoweixijiefenxi,hbrh9640,www04544com,www.08988.cp.com,wan9665.com,www.douyinse.com,ah0389,js1188,vns7503com,qpby8844,WWW.218.COM,wwwkk464646com,rr77149com,4501bet,s5185.com,yyailu,www.hg0247.com,777277hhcom,hg8245com,tangyefei,www.5564y.net,hongxial12@yahoo.cn,36pao,d948d.com,www.49365.cc,qifa991com,618msc.com,www.8888mv.com,9044365.com,2O48hd,,ks6835.com,www.hg04598.com,tiyutouzhuguanwang,wwwddtdcn,WWW48999COM_WWW.48999,COM,41669.com,www.js2212.com,11177381.com,www.tyc399.com,852905com,2964845458@qq.com,www.95abcd.com,imicom官网解锁,www.mkt.8694z.com,www.3335018.com,www.xpj4816.com,dafa555net,xpj00567.com,wwwxpj0122com,wwwpujin,3580404.com,www32327158com,38336655.com,www.5151.hhcom,www.ete2013.com,www123365sbcom,xdh18.com,vns9478com,www.zhiwoo.cn,www.hd0107.cc,yh9158.com,www.1869977.com,www.a1a222.cc,www.pj6608.com,www.400400.com,WWW.7990.COM,321666com,xuexiuzhong,www.9980099.com,32177.com,44wyt,zhangqihua,www.hg7175.net,ule891.com,pg930.com,541852828,xpj66656.com,xiaoming14.com,sdfus123,ab1733.com,beisitequanqiuzuishehua2222,ag5141com,wwwfa818com,www850702com,www.49579..com,www.81365a.com,vip58ganjicom,ww.haosf.com,www.51yes.com,www.251144.com,456652135@qq.com,www332hkcom,335678.com,www.p888111.com,0746vip.com,www.955078.com,www195mscCOM,www.lesnedu.com,lxx001,www.78854.com,31c31o.vip,www.81699n.com,867024com,5577f.com,wwwv3433com,www.402w1.com,美国大片免费电影网站http://77k.0033.cn,tyc1910.com,99fbcom,www.901suncity.com,www.drf0911.com,hg4012.com,www.9946y.con,www.blg008.com,www.se42.com,a8044com,888907b.com,474w6.com,hy588|

www.yh654.net,www.yh201811.com,www.sc088.com,03331.com,oumeigaoqingvivoesond,jbb23.cc,www.3636qq .com,ygx123,www.99ff4.con,5360hh,cr1820.com,www.953cf.com,447abc.com,xierui520,817ks.net,uua58.cc,75bo.com,*pingbideguanjianzi*wangzhanzaixian,tycw90,1397v.vom,www.885suncity.com,www.tt807.com,www.9086gg.com,846669com,www.tk718.com,http://qigekeji.cccpan.com,wwwv33333com,香港新版挂牌网址,www.pj7228.com,bet888365com,www.sj66966.com,wwwbbs78068com,www.495751.com,97o376.net,yabo850.com,WWW.002BET365.COM,6688ghjk,wwwcx1817com,www.8844dd.com,wwwj88333com,www.3665.bet,www.15425.com,aisex.com,wwws666888com,henhenlutupianzhuanqu,www.77745.com,www.hm0026.com,xiakai198748,WWW.808BTT.COM,www.524432.com,WWW.R8388.COM,sifangbobose,www868fcom,www.mgm.am,www.065.com,96674,com,www.33dxdx.com,cp8696com,szy888,www.a39814.com,www.m.09f.cm,5x性社区免费视频播,zhang88,wwwbm6306com,2970lb.com,889988com,ky1004,m1248fcc,yf100.com,kk0022.com,www.4080,wwwnew511com,Www.3344ra.,vod588.com,www.cc5555.com,8x8xk58b,WWW.AG.10050763.COM,wwwet7900com,hl310183740,tieganguojiyulecheng,www.550666.com,www9hwxcom,wwwceo558com,980wyt.com,wwww67802com,simitupian,hg9779.com,www.7893w53.com,js733.com,7402.ag,jiali123,jj9199,840905,www.kkkk80.com,guotengzhun@163.com,wwwmg4722com,www46hczlcom,1888123.com,yb4940.com,www.6582205.com,www.lvmaofq.com/[/url][,qiuguazhashipin,w66.org,www.rf62.com,wwwssc66611com,ks9669com,7227.con,www.wsdc8899.com,oo29298,www112558COM,m.99vv1.cn,www.w8797.com,pixsky.com,ah.2-calss.com,247777.com,yabo4361.com,草馏,www.75tyc.com,wwwtyc306com,blm8866.com,wang778,wei80,www.7819.com,www.amjsgw8.com,5581r.com,WWW,78953,com,hg4055.com,www.992299.com,shtx.manmankan.com,qingqingcaoshipinmianfeiguankan,1973v.com,bet36527365333.com,www.448658.com,www.www.919009.com,www15dddcom,sanya5555.com,2682002019@qq.com,wwwbet365318com,flbktrk.comwww.www238CⅰCO,www.hg1231.net,grhr,www.44hf44.com,mogee.com,www.55463.com,t7e45u,nuoya486.com,drink77.com,WWW.D22.COM,shachao888,ag81151.com,www.9968msc.com,www.a1a555.cc,www.lh555.com,www30019wcom,wwwkk446com,www838667com,www.2213h.com,113215.com,www.hongli4.com,ww886.com,www05088bet,www.js66880.com,jjbzzy2,wwwyh19118com,ks8118.vip,liao65430171,wwwcddworldtourcom,www.tube8.com|

以上会员名单排名不分前后

相关文档

3.3函数的和、差、积、商的导数(二)
函数的和差积商的导数二
和差积商与复合函数的导数(2)
第6课时 3.2.2函数的和、差、积、商的导数
高二数学函数的和差积商的导数2
1.2.2《函数的和、差、积、商的导数》课件
3.2.2《函数的和、差、积、商的导数》课件(苏教版1-1)
苏教版高中数学(选修1-1)3.2《导数的运算》(函数的和、差、积、商的导数)
3.2.2 函数的和、差、积、商的导数 课件(苏教版选修1-1)
数学:1.2.2《函数的和、差、积、商的导数》课件(苏教版选修2-2)
学霸百科
68510368文学网 685103681php网站 685103682jsp网站 685103683小说站 685103684算命网 685103685占卜网 685103686星座网