《高等數(shù)學(xué)基礎(chǔ)》形成性考核作業(yè)2答案

《高等數(shù)學(xué)基礎(chǔ)》形成性考核作業(yè)2答案第三章導(dǎo)數(shù)與微分一、單項(xiàng)選擇題1.B2.D3.A4.D5.C二、填空題0；2lnx5；3．；4．；；6．.112xx1y102x2xx三、計(jì)算題1.求下列函數(shù)的導(dǎo)數(shù)：y3313(1)解：yx3eyxex3e2x2x2x21即yexx3x6.x21112解：y2xlnxx2xlnx.2sinxxsinx2211x3解：y2xxxx1.2xxx2214解：yx22x3xx2x32x6x21xxx.xx23x4x4115解：y2xsinxlnxxcosx2sinxx212xxlnx22cos.xsinxsinx2sinx6y4xcosxlnx.3x第1頁(yè)共4頁(yè)17解：y3x2x3ln3sinxx22xx3x1x2xsinxln3xln3.23x118解：yexexxxx211ex.xxx22.求下列函數(shù)的導(dǎo)數(shù)：y11yexe.xx2x1sinx2解：ycosxtan.cosxcosx1127127123解：yxxxxyx.8884解：yxxxx2.（5）解y'(x)cosx2xcosx2226解：y=-sineeesine.xxxx7解：ynsinxxcossinxsinnn1nnsinxxcossinxsinnsinxn1.n1n18解：y5ln5x5xlnxx9解：yex.xx3.在下列方程中，是由方程確定的函數(shù)，求：yyxy1解：ycosxysinxe2y,2ycosyxsin,2yyxeysinxy.cosxe2y第2頁(yè)共4頁(yè)cosy2解：ysinyylnx,xcosy1sinylnxy,xcosyy.x1sinylnxx3解：ysiny,兩邊求導(dǎo)，得21sincos,yyyyy21y.2sinyycosy1y4解：yy1.yy15ey2yy,yx12yey,yx1y.x2yey6解：2yyesinyecosyy,xx2yecosyyesiny,xxesinyxy.2yecosyx7解：eye3yy,yx2e3yye,y2xexe3yy.y28y5ln52ln2y,xy12ln2y5ln5,yx5ln5xy.12ln2y4.求下列函數(shù)的微分：dy1yxxxxxx,22yxxx.第3頁(yè)共4頁(yè)1sinxcosxlnxsinxxcosxlnx2解：yx,sinxxsinx22sinxxcosxlnxdydx.xsinx23解：y2sinxcosxsin2x,dysin2xdx.4解：yseceeesecx,2xxx2dyesecxdx.x25.求下列函數(shù)的二階導(dǎo)數(shù)：111解：yx1,22x2111yx3x3.222242y3ln3,xy3ln3.x213解：y,x1y.2x4ysinxxx,yxxxsinxxxsin.四、證明題證：由題設(shè)，有fxfx,