高数微积分公式大全,高数微积分公式大全24个

('高等数学微积分公式大全一、基本导数公式⑴\uf028\uf0290c\uf0a2\uf03d⑵1xx\uf06d\uf06d\uf06d\uf02d\uf03d⑶\uf028\uf029sincosxx\uf0a2\uf03d⑷\uf028\uf029cossinxx\uf0a2\uf03d\uf02d⑸\uf028\uf0292tansecxx\uf0a2\uf03d⑹\uf028\uf0292cotcscxx\uf0a2\uf03d\uf02d⑺\uf028\uf029secsectanxxx\uf0a2\uf03d\uf0d7⑻\uf028\uf029csccsccotxxx\uf0a2\uf03d\uf02d\uf0d7⑼\uf028\uf029xxee\uf0a2\uf03d⑽\uf028\uf029lnxxaaa\uf0a2\uf03d⑾\uf028\uf0291lnxx\uf0a2\uf03d⑿\uf028\uf0291loglnxaxa\uf0a2\uf03d⒀\uf028\uf02921arcsin1xx\uf0a2\uf03d\uf02d⒁\uf028\uf02921arccos1xx\uf0a2\uf03d\uf02d\uf02d⒂\uf028\uf02921arctan1xx\uf0a2\uf03d\uf02b⒃\uf028\uf02921arccot1xx\uf0a2\uf03d\uf02d\uf02b⒄\uf028\uf0291x\uf0a2\uf03d⒅\uf028\uf02912xx\uf0a2\uf03d二、导数的四则运算法则\uf028\uf029uvuv\uf0a2\uf0a2\uf0a2\uf0b1\uf03d\uf0b1\uf028\uf029uvuvuv\uf0a2\uf0a2\uf0a2\uf03d\uf02b2uuvuvvv\uf0a2\uf0a2\uf0a2\uf02d\uf0e6\uf0f6\uf03d\uf0e7\uf0f7\uf0e8\uf0f8三、高阶导数的运算法则（1）\uf028\uf029\uf028\uf029\uf028\uf029\uf028\uf029\uf028\uf029\uf028\uf029\uf028\uf029nnnuxvxuxvx\uf0b1\uf03d\uf0b1\uf0e9\uf0f9\uf0eb\uf0fb（2）\uf028\uf029\uf028\uf029\uf028\uf029\uf028\uf029nncuxcux\uf03d\uf0e9\uf0f9\uf0eb\uf0fb（3）\uf028\uf029\uf028\uf029\uf028\uf029\uf028\uf029nnnuaxbauaxb\uf02b\uf03d\uf02b\uf0e9\uf0f9\uf0eb\uf0fb（4）\uf028\uf029\uf028\uf029\uf028\uf029\uf028\uf029\uf028\uf029\uf028\uf029()0nnnkkknkuxvxcuxvx\uf02d\uf03d\uf0d7\uf03d\uf0e9\uf0f9\uf0eb\uf0fb\uf0e5四、基本初等函数的n阶导数公式（1）\uf028\uf029\uf028\uf029!nnxn\uf03d（2）\uf028\uf029\uf028\uf029naxbnaxbeae\uf02b\uf02b\uf03d\uf0d7(3)\uf028\uf029\uf028\uf029lnnxxnaaa\uf03d(4)\uf028\uf029\uf028\uf029sinsin2nnaxbaaxbn\uf070\uf0e6\uf0f6\uf02b\uf03d\uf02b\uf02b\uf0d7\uf0e9\uf0f9\uf0e7\uf0f7\uf0eb\uf0fb\uf0e8\uf0f8(5)\uf028\uf029\uf028\uf029coscos2nnaxbaaxbn\uf070\uf0e6\uf0f6\uf02b\uf03d\uf02b\uf02b\uf0d7\uf0e9\uf0f9\uf0e7\uf0f7\uf0eb\uf0fb\uf0e8\uf0f8(6)\uf028\uf029\uf028\uf029\uf028\uf02911!1nnnnanaxbaxb\uf02b\uf0d7\uf0e6\uf0f6\uf03d\uf02d\uf0e7\uf0f7\uf02b\uf0e8\uf0f8\uf02b(7)\uf028\uf029\uf028\uf029\uf028\uf029\uf028\uf029\uf028\uf02911!ln1nnnnanaxbaxb\uf02d\uf0d7\uf02d\uf02b\uf03d\uf02d\uf0e9\uf0f9\uf0eb\uf0fb\uf02b五、微分公式与微分运算法则⑴\uf028\uf0290dc\uf03d⑵\uf028\uf0291dxxdx\uf06d\uf06d\uf06d\uf02d\uf03d⑶\uf028\uf029sincosdxxdx\uf03d⑷\uf028\uf029cossindxxdx\uf03d\uf02d⑸\uf028\uf0292tansecdxxdx\uf03d⑹\uf028\uf0292cotcscdxxdx\uf03d\uf02d⑺\uf028\uf029secsectandxxxdx\uf03d\uf0d7⑻\uf028\uf029csccsccotdxxxdx\uf03d\uf02d\uf0d7⑼\uf028\uf029xxdeedx\uf03d⑽\uf028\uf029lnxxdaaadx\uf03d⑾\uf028\uf0291lndxdxx\uf03d⑿\uf028\uf0291loglnxaddxxa\uf03d⒀\uf028\uf02921arcsin1dxdxx\uf03d\uf02d⒁\uf028\uf02921arccos1dxdxx\uf03d\uf02d\uf02d⒂\uf028\uf02921arctan1dxdxx\uf03d\uf02b⒃\uf028\uf02921arccot1dxdxx\uf03d\uf02d\uf02b六、微分运算法则⑴\uf028\uf029duvdudv\uf0b1\uf03d\uf0b1⑵\uf028\uf029dcucdu\uf03d⑶\uf028\uf029duvvduudv\uf03d\uf02b⑷2uvduudvdvv\uf02d\uf0e6\uf0f6\uf03d\uf0e7\uf0f7\uf0e8\uf0f8七、基本积分公式⑴kdxkxc\uf03d\uf02b\uf0f2⑵11xxdxc\uf06d\uf06d\uf06d\uf02b\uf03d\uf02b\uf02b\uf0f2⑶lndxxcx\uf03d\uf02b\uf0f2⑷lnxxaadxca\uf03d\uf02b\uf0f2⑸xxedxec\uf03d\uf02b\uf0f2⑹cossinxdxxc\uf03d\uf02b\uf0f2⑺sincosxdxxc\uf03d\uf02d\uf02b\uf0f2⑻221sectancosdxxdxxcx\uf03d\uf03d\uf02b\uf0f2\uf0f2⑼221csccotsinxdxxcx\uf03d\uf03d\uf02d\uf02b\uf0f2\uf0f2⑽21arctan1dxxcx\uf03d\uf02b\uf02b\uf0f2⑾21arcsin1dxxcx\uf03d\uf02b\uf02d\uf0f2八、补充积分公式tanlncosxdxxc\uf03d\uf02d\uf02b\uf0f2cotlnsinxdxxc\uf03d\uf02b\uf0f2seclnsectanxdxxxc\uf03d\uf02b\uf02b\uf0f2csclncsccotxdxxxc\uf03d\uf02d\uf02b\uf0f22211arctanxdxcaxaa\uf03d\uf02b\uf02b\uf0f22211ln2xadxcxaaxa\uf02d\uf03d\uf02b\uf02d\uf02b\uf0f2221arcsinxdxcaax\uf03d\uf02b\uf02d\uf0f222221lndxxxacxa\uf03d\uf02b\uf0b1\uf02b\uf0b1\uf0f2九、下列常用凑微分公式积分型换元公式\uf028\uf029\uf028\uf029\uf028\uf0291faxbdxfaxbdaxba\uf02b\uf03d\uf02b\uf02b\uf0f2\uf0f2uaxb\uf03d\uf02b\uf028\uf029\uf028\uf029\uf028\uf02911fxxdxfxdx\uf06d\uf06d\uf06d\uf06d\uf06d\uf02d\uf03d\uf0f2\uf0f2ux\uf06d\uf03d\uf028\uf029\uf028\uf029\uf028\uf0291lnlnlnfxdxfxdxx\uf0d7\uf03d\uf0f2\uf0f2lnux\uf03d\uf028\uf029\uf028\uf029\uf028\uf029xxxxfeedxfede\uf0d7\uf03d\uf0f2\uf0f2xue\uf03d\uf028\uf029\uf028\uf029\uf028\uf0291lnxxxxfaadxfadaa\uf0d7\uf03d\uf0f2\uf0f2xua\uf03d\uf028\uf029\uf028\uf029\uf028\uf029sincossinsinfxxdxfxdx\uf0d7\uf03d\uf0f2\uf0f2sinux\uf03d\uf028\uf029\uf028\uf029\uf028\uf029cossincoscosfxxdxfxdx\uf0d7\uf03d\uf02d\uf0f2\uf0f2cosux\uf03d\uf028\uf029\uf028\uf029\uf028\uf0292tansectantanfxxdxfxdx\uf0d7\uf03d\uf0f2\uf0f2tanux\uf03d\uf028\uf029\uf028\uf029\uf028\uf0292cotcsccotcotfxxdxfxdx\uf0d7\uf03d\uf0f2\uf0f2cotux\uf03d\uf028\uf029\uf028\uf029\uf028\uf02921arctanarcnarcn1fxdxftaxdtaxx\uf0d7\uf03d\uf02b\uf0f2\uf0f2arctanux\uf03d\uf028\uf029\uf028\uf029\uf028\uf02921arcsinarcsinarcsin1fxdxfxdxx\uf0d7\uf03d\uf02d\uf0f2\uf0f2arcsinux\uf03d十、分部积分法公式⑴形如naxxedx\uf0f2，令nux\uf03d，axdvedx\uf03d形如sinnxxdx\uf0f2令nux\uf03d，sindvxdx\uf03d形如cosnxxdx\uf0f2令nux\uf03d，cosdvxdx\uf03d⑵形如arctannxxdx\uf0f2，令arctanux\uf03d，ndvxdx\uf03d形如lnnxxdx\uf0f2，令lnux\uf03d，ndvxdx\uf03d⑶形如sinaxexdx\uf0f2，cosaxexdx\uf0f2令,sin,cosaxuexx\uf03d均可。十一、第二换元积分法中的三角换元公式(1)22ax\uf02dsinxat\uf03d(2)22ax\uf02btanxat\uf03d(3)22xa\uf02dsecxat\uf03d【特殊角的三角函数值】（1）sin00\uf03d（2）1sin62\uf070\uf03d（3）3sin32\uf070\uf03d（4）sin12\uf070\uf03d）（5）sin0\uf070\uf03d（1）cos01\uf03d（2）3cos62\uf070\uf03d（3）1cos32\uf070\uf03d（4）cos02\uf070\uf03d）（5）cos1\uf070\uf03d\uf02d（1）tan00\uf03d（2）3tan63\uf070\uf03d（3）tan33\uf070\uf03d（4）tan2\uf070不存在（5）tan0\uf070\uf03d（1）cot0不存在（2）cot36\uf070\uf03d（3）3cot33\uf070\uf03d（4）cot02\uf070\uf03d（5）cot\uf070不存在十二、重要公式（1）0sinlim1xxx\uf0ae\uf03d（2）\uf028\uf02910lim1xxxe\uf0ae\uf02b\uf03d（3）lim()1nnaao\uf0ae\uf0a5\uf03e\uf03d（4）lim1nnn\uf0ae\uf0a5\uf03d（5）limarctan2xx\uf070\uf0ae\uf0a5\uf03d（6）limtan2xarcx\uf070\uf0ae\uf02d\uf0a5\uf03d\uf02d（7）limarccot0xx\uf0ae\uf0a5\uf03d（8）limarccotxx\uf070\uf0ae\uf02d\uf0a5\uf03d（9）lim0xxe\uf0ae\uf02d\uf0a5\uf03d（10）limxxe\uf0ae\uf02b\uf0a5\uf03d\uf0a5（11）0lim1xxx\uf02b\uf0ae\uf03d（12）00101101lim0nnnmmxmanmbaxaxanmbxbxbnm\uf02d\uf02d\uf0ae\uf0a5\uf0ec\uf03d\uf0ef\uf0ef\uf02b\uf02b\uf02b\uf0ef\uf03d\uf03c\uf0ed\uf02b\uf02b\uf02b\uf0ef\uf0a5\uf03e\uf0ef\uf0ef\uf0ee\uf04c\uf04c（系数不为0的情况）十三、下列常用等价无穷小关系（0x\uf0ae）sinxx\uf03atanxx\uf03aarcsinxx\uf03aarctanxx\uf03a211cos2xx\uf02d\uf03a\uf028\uf029ln1xx\uf02b\uf03a1xex\uf02d\uf03a1lnxaxa\uf02d\uf03a\uf028\uf02911xx\uf0b6\uf02b\uf02d\uf0b6\uf03a十四、三角函数公式1.两角和公式sin()sincoscossinABABAB\uf02b\uf03d\uf02bsin()sincoscossinABABAB\uf02d\uf03d\uf02dcos()coscossinsinABABAB\uf02b\uf03d\uf02dcos()coscossinsinABABAB\uf02d\uf03d\uf02btantantan()1tantanABABAB\uf02b\uf02b\uf03d\uf02dtantantan()1tantanABABAB\uf02d\uf02d\uf03d\uf02bcotcot1cot()cotcotABABBA\uf0d7\uf02d\uf02b\uf03d\uf02bcotcot1cot()cotcotABABBA\uf0d7\uf02b\uf02d\uf03d\uf02d2.二倍角公式sin22sincosAAA\uf03d2222cos2cossin12sin2cos1AAAAA\uf03d\uf02d\uf03d\uf02d\uf03d\uf02d22tantan21tanAAA\uf03d\uf02d3.半角公式1cossin22AA\uf02d\uf03d1coscos22AA\uf02b\uf03d1cossintan21cos1cosAAAAA\uf02d\uf03d\uf03d\uf02b\uf02b1cossincot21cos1cosAAAAA\uf02b\uf03d\uf03d\uf02d\uf02d4.和差化积公式sinsin2sincos22ababab\uf02b\uf02d\uf02b\uf03d\uf0d7sinsin2cossin22ababab\uf02b\uf02d\uf02d\uf03d\uf0d7coscos2coscos22ababab\uf02b\uf02d\uf02b\uf03d\uf0d7coscos2sinsin22ababab\uf02b\uf02d\uf02d\uf03d\uf02d\uf0d7\uf028\uf029sintantancoscosababab\uf02b\uf02b\uf03d\uf0d75.积化和差公式\uf028\uf029\uf028\uf0291sinsincoscos2ababab\uf03d\uf02d\uf02b\uf02d\uf02d\uf0e9\uf0f9\uf0eb\uf0fb\uf028\uf029\uf028\uf0291coscoscoscos2ababab\uf03d\uf02b\uf02b\uf02d\uf0e9\uf0f9\uf0eb\uf0fb\uf028\uf029\uf028\uf0291sincossinsin2ababab\uf03d\uf02b\uf02b\uf02d\uf0e9\uf0f9\uf0eb\uf0fb\uf028\uf029\uf028\uf0291cossinsinsin2ababab\uf03d\uf02b\uf02d\uf02d\uf0e9\uf0f9\uf0eb\uf0fb6.万能公式22tan2sin1tan2aaa\uf03d\uf02b221tan2cos1tan2aaa\uf02d\uf03d\uf02b22tan2tan1tan2aaa\uf03d\uf02d7.平方关系22sincos1xx\uf02b\uf03d22secn1xtax\uf02d\uf03d22csccot1xx\uf02d\uf03d8.倒数关系tancot1xx\uf0d7\uf03dseccos1xx\uf0d7\uf03dcsin1csxx\uf0d7\uf03d9.商数关系sintancosxxx\uf03dcoscotsinxxx\uf03d十五、几种常见的微分方程1.可分离变量的微分方程：\uf028\uf029\uf028\uf029dyfxgydx\uf03d，\uf028\uf029\uf028\uf029\uf028\uf029\uf028\uf02911220fxgydxfxgydy\uf02b\uf03d2.齐次微分方程：dyyfdxx\uf0e6\uf0f6\uf03d\uf0e7\uf0f7\uf0e8\uf0f83.一阶线性非齐次微分方程：\uf028\uf029\uf028\uf029dypxyQxdx\uf02b\uf03d解为：\uf028\uf029\uf028\uf029\uf028\uf029pxdxpxdxyeQxedxc\uf02d\uf0e9\uf0f9\uf0f2\uf0f2\uf03d\uf02b\uf0ea\uf0fa\uf0eb\uf0fb\uf0f2',)