您好,欢迎访问三七文档
当前位置:首页 > 中学教育 > 高中教育 > 微积分及三角函数公式合集
第一部分:常用积分公式基本积分公式:1kdxkxc211xxdxc3lndxxcx4lnxxaadxca5xxedxec6cossinxdxxc7sincosxdxxc8221sectancosdxxdxxcx9221csccotsinxdxxcx1021arctan1dxxcx1121arcsin1dxxcx12tanlncosxdxxc13cotlnsinxdxxc14seclnsectanxdxxxc15csclncsccotxdxxxc162211arctanxdxcaxaa172211ln2xadxcxaaxa18221arcsinxdxcaax1922221lndxxxacxa分部积分法公式1形如naxxedx,令nux,axdvedx2形如sinnxxdx令nux,sindvxdx3形如cosnxxdx令nux,cosdvxdx4形如arctannxxdx,令arctanux,ndvxdx5形如lnnxxdx,令lnux,ndvxdx6形如sinaxexdx,cosaxexdx令,sin,cosaxuexx均可。常用凑微分公式1.1faxbdxfaxbdaxba2.11fxxdxfxdx3.1lnlnlnfxdxfxdxx4.xxxxfeedxfede5.1lnxxxxfaadxfadaa6.sincossinsinfxxdxfxdx7.cossincoscosfxxdxfxdx8.2tansectantanfxxdxfxdx9.1()2()()fxdxfxdxx10.21111()()()fdxfdxxxx11.2cotcsccotcotfxxdxfxdx第二部分:常用微分、导数公式(c=常数)1、极限(1)0sinlim1xxx(2)10lim1xxxe(3)lim()1nnaao(4)lim1nnn(5)limarctan2xx(6)limtan2xarcx(7)limarccot0xx(8)limarccotxx(9)lim0xxe(10)limxxe(11)0lim1xxx(12)00101101lim0nnnmmxmanmbaxaxanmbxbxbnm(系数不为0的情况)(13)000()()limxxxxfxfxyx2、常用等价无穷小关系(0x)sin~xxtan~xxarcsin~xxarctan~xx211cos~2xxln1~xx1~xex1~lnxaxa11~xx21sec1~2xx211sin1~2xxx22211~xxx33sin~()xx3、导数的四则运算法则uvuvuvuvuv2uuvuvvv4、基本导数公式⑴0c⑵1xx⑶sincosxx⑷cossinxx⑸2tansecxx⑹2cotcscxx⑺secsectanxxx⑻csccsccotxxx⑼xxee⑽lnxxaaa⑾1lnxx⑿1loglnxaxa⒀21arcsin1xx⒁21arccos1xx⒂21arctan1xx⒃21arccot1xx⒄1x⒅12xx5、高阶导数的运算法则(1)nnnuxvxuxvx(2)nncuxcux(3)nnnuaxbauaxb(4)()0nnnkkknkuxvxcuxvx6、基本初等函数的n阶导数公式(1)!nnxn(2)naxbnaxbeae(3)lnnxxnaaa(4)sinsin2nnaxbaaxbn(5)coscos2nnaxbaaxbn(6)11!1nnnnanaxbaxb(7)11!ln1nnnnanaxbaxb7、微分公式与微分运算法则⑴0dc⑵1dxxdx⑶sincosdxxdx⑷cossindxxdx⑸2tansecdxxdx⑹2cotcscdxxdx⑺secsectandxxxdx⑻csccsccotdxxxdx⑼xxdeedx⑽lnxxdaaadx⑾1lndxdxx⑿1loglnxaddxxa⒀21arcsin1dxdxx⒁21arccos1dxdxx⒂21arctan1dxdxx⒃21arccot1dxdxx8、微分运算法则⑴duvdudv⑵dcucdu⑶duvvduudv⑷2uvduudvdvv第三部分:常用三角函数公式1.和差公式sin()sincoscossinABABABsin()sincoscossinABABABcos()coscossinsinABABABcos()coscossinsinABABABtantantan()1tantanABABABtantantan()1tantanABABABcotcot1cot()cotcotABABBAcotcot1cot()cotcotABABBA2.倍角公式sin22sincosAAA2222cos2cossin12sin2cos1AAAAA22tantan21tanAAA3.半角公式1cossin22AA1coscos22AA1cossintan21cos1cosAAAAA1cossincot21cos1cosAAAAA4.和差化积公式sinsin2sincos22abababsinsin2cossin22abababcoscos2coscos22abababcoscos2sinsin22abababsintantancoscosababab5.积化和差公式1sinsincoscos2ababab1coscoscoscos2ababab1sincossinsin2ababab1cossinsinsin2ababab6.万能公式22tan2sin1tan2aaa221tan2cos1tan2aaa22tan2tan1tan2aaa7.平方关系22sincos1xx22secn1xtax22csccot1xx8.倒数关系tancot1xxseccos1xxcsin1csxx9.商数关系sintancosxxxcoscotsinxxx10.正弦定理:RCcBbAa2sinsinsin11.余弦定理:Cabbaccos222212.反三角函数性质:arcctgxarctgxxx2arccos2arcsin
本文标题:微积分及三角函数公式合集
链接地址:https://www.777doc.com/doc-5474911 .html