《導(dǎo)數(shù)與微分2》ppt課件(文件)
【正文】 ??????????????）令（導(dǎo)數(shù)與微分 xxxxxtvuxtvuyxttvvuuyxy2c os14s i n2c os12c os2s i n22)s i n(221)2()( c os1()(2,c os,1,:2c os16)22222???????????????????????????）令（導(dǎo)數(shù)與微分 )(ln2)(ln2)(()(,),(:)()(7)22222xxvvvxafaxaufaxaxaufyxvauufyafuf???????????????????）令的導(dǎo)數(shù)存在，求已知（導(dǎo)數(shù)與微分 ? 例 5：證明：偶函數(shù)的導(dǎo)數(shù)是奇函數(shù)。 ? 證：設(shè) f(x)是偶函數(shù)，即 f(x)=f(x) u=x 是偶函數(shù)。注：微分公式可以與求dxxxddxxxddxxdar c c t gxdxxdar c t gxdxxxddxxxdc s e x c t gx dxdc s e xx t gx dxxd2222211)19(21)18(11)17(11)16(11a r c c os)15(11a r c s i n)14()13(s e cs e c)12(????????????????導(dǎo)數(shù)與微分 ? 0)()()()(2?????????vvu dvv dudcc ducudu dvv duuvddvduvudvu為常數(shù)導(dǎo)數(shù)與微分 例 10 求下列函數(shù)的微分： dxxxxxdxxxx dxnxxxdxxdxxddyxxydxxxex dxedxexxdex dexdedyxeyxxxxxxx)s i nc os( l ns i nc oslns i ns i nlnlns i nlns i n)2()s i n( c oss i nc osc osc osc osc os)1(??????????????????導(dǎo)數(shù)與微分 dxxt gxxxxdxt gxx dxxxxt gx dx dt gxxt gxddyxt gxyxx2122122lns e clnlns e clnlnlnlnlnln3)???????????（導(dǎo)數(shù)與微分 ： 若 u為自變量 ,y＝ f(u),則 , 若 u為中間變量 , 從而不論 u是自變量還是中間變量其微分的形式不變 ,皆為dy=f’(x)du. 我們將微分的這一性質(zhì)稱為一階微分形式不變性 利用一階微分形式不變性可以方便的求出復(fù)合函 數(shù)和隱函數(shù)的微分和導(dǎo)數(shù)。w) z0C4F7I aMdPhSkVnZq$t*x A2D5G8KbNeQiTlWor%v( y+B3E6H9LcOgRjUmYp!samp。v)z0C3F7IaLdPgSkVnYq$t*wA1D5G 8JbNeQhTlWoZr %u(y+B2E6H9KcOfRjUm Xp! samp。w z1C4G7JbMePhTkWnZr$u( x+A2E5H8KcNfRiUlXps%v) y0C3F6I aLdOgSjVnYq! t*wz1D4G7JbMeQhTkWoZr$u(x+B2E5H9KcNfRiUm Xpsamp。w) z1C4F7JaM ePhSkWnZq$u*x+A2D9LcOfRjUmYp!samp。v)y0C3F6IaLdPgSjVnYq!t *w A1D4G8JbMeQhTlWoZr %u(x+B2E6H9KcOfRiUm Xpsamp。w) z0C4F7I aMdPgSkVnZq$t*x A1D5G8KbNeQiTlWor%v( y+B3E6H9LcOgRjUmYp!samp。w) z1C4G7JaMePhSkWnZr$u*x+A2D5H8KcNfQiUlXos%v) y0B3F6I 9LdOgRjVm Yq!t amp。w) z0C4F7JaMdPhSkVnZq$u*x A2D5G8KbNfQiTlXor%v( y+B3E6I 9LcOgRjUm Yp! tamp。w z1C4G7JaMePhTkWnZr$u*x+A2E5H8KcNfQiUlXps%v) y0B3F6IaLdOgSjVmYq!t*wz1D4G7JbM eQhTkWoZr $u( x+B2E5H9KcNf RiUlXpsamp。w)z1C4F7JaMXpsamp。w) z1C4F7JaM dPhSkWnZq$u*xA2D5H8KbNf Q iTlXos%v(y0B3E6I9LcOgRjVmYp! tamp。wz1C4G7JbMePhTkWnZr$u(x+A2E5H8KcNfRiUlXps%v) y0C3F6I aLdOgSjVnYq!t*wz1D4G8JbMeQhTkWoZr %u( x+B2E5H9KcNfRiUmXpsamp。v)z0C3F7IaMdPgSkVnYq$t *xA1D5G8JbNeQiTlWor %u(y+B3E6H9LcOfRjUm Yp!samp。w z1C4G7JaMePhTkWnZr$u+B3E6I 9LcOgRjUm Yp! tamp。w) z0C4F7I aMdPhSkVnZq$t*x A2D5G8KbNeQiTlWor%v( y+B3E6H9LcOgRjUmYp!samp。w) z1C4F7JaMdPhSkWnZq$u*xA2D5H8KbNf QiTlXor %v(y0B3E6I9LcOgRjVmYp! tamp。wz1C4GRjUm Xp! samp。w) z1C4F7JaMePhSkWnZq$u*x+A2D5H8KVnYq$t*wA1D4G 8JbNeQhTlWoZr %u(y+B2E6H9KcOfRiUm Xp! samp。w) z0C4F7IaMdPhSk 。w)z0C4F7JaMdPhSkVnZq$x+B2E6H9KcOf RiUmXp!samp。w) z0C4F7JaM dPhSkVnZq$u*xA2D5G8KbNfQiTlXor%v(y0B3E6I9LcOgRjVmYpx A1D5G8JbNeQiTlWor%u( y+B3E6H9LcOfRjUm Yp! samp。w)z1C4F7JaMdPhSkVnZq$u*xA2D5G 8KbNf QiTlXor %v(y0B3E6I 9LcOgRjVm Yp! tamp。w)z1C4F7JaMdPhSkWnZq$u*xA2D5H8KbNfQiTlXos%v( y0B3E6I9LcOgRjVmYp!tamp。w z1C4G7JaMePhTkWnZr$u*x+A2E5H8KcNfQiUlXps%v) y0B3F6I9LdOgSjVmYq!tamp。w)z0C4F7IaMdPhSkVnZq$t *xA2D5G 8KbNeQiTlXor%v(y+B3E6I9LcOgRjUmYp!t amp。v)z0C4F7IaMdPgSkVnZq$t*xA1D5G 8JbNeQiTlWor%u( y+B3E6PhTkWnZr $u(x+A2E5H8KcNfRiUlXps%v)y0C3
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