积分与求导公式大全

一、导数的四则运算法则uvuvuvuvuv2uuvuvvv二、基本导数公式⑴0c⑵1xx⑶sincosxx⑷cossinxx⑸2tansecxx⑹2cotcscxx⑺secsectanxxx⑻csccsccotxxx⑼xxee⑽lnxxaaa⑾1lnxx⑿1loglnxaxa⒀21arcsin1xx⒁21arccos1xx⒂21arctan1xx⒃21arccot1xx⒄1x⒅12xx三、高阶导数的运算法则（1）nnnuxvxuxvx（2）nncuxcux（3）nnnuaxbauaxb（4）()0nnnkkknkuxvxcuxvx四、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!ln1nnnnanaxbaxb五、微分公式与微分运算法则⑴0dc⑵1dxxdx⑶sincosdxxdx⑷cossindxxdx⑸2tansecdxxdx⑹2cotcscdxxdx⑺secsectandxxxdx⑻csccsccotdxxxdx⑼xxdeedx⑽lnxxdaaadx⑾1lndxdxx⑿1loglnxaddxxa⒀21arcsin1dxdxx⒁21arccos1dxdxx⒂21arctan1dxdxx⒃21arccot1dxdxx六、微分运算法则⑴duvdudv⑵dcucdu⑶duvvduudv⑷2uvduudvdvv七、基本积分公式⑴kdxkxc⑵11xxdxc⑶lndxxcx⑷lnxxaadxca⑸xxedxec⑹cossinxdxxc⑺sincosxdxxc⑻221sectancosdxxdxxcx⑼221csccotsinxdxxcx⑽21arctan1dxxcx⑾21arcsin1dxxcxtanlncosxdxxccotlnsinxdxxcseclnsectanxdxxxccsclncsccotxdxxxc2211arctanxdxcaxaa2211ln2xadxcxaaxa221arcsinxdxcaax22221lndxxxacxa八、下列常用凑微分公式积分型换元公式1faxbdxfaxbdaxbauaxb11fxxdxfxdxux1lnlnlnfxdxfxdxxlnuxxxxxfeedxfedexue1lnxxxxfaadxfadaaxuasincossinsinfxxdxfxdxsinuxcossincoscosfxxdxfxdxcosux2tansectantanfxxdxfxdxtanux2cotcsccotcotfxxdxfxdxcotux21arctanarcnarcn1fxdxftaxdtaxxarctanux21arcsinarcsinarcsin1fxdxfxdxxarcsinux九、分部积分法公式⑴形如naxxedx，令nux，axdvedx形如sinnxxdx令nux，sindvxdx形如cosnxxdx令nux，cosdvxdx⑵形如arctannxxdx，令arctanux，ndvxdx形如lnnxxdx，令lnux，ndvxdx⑶形如sinaxexdx，cosaxexdx令,sin,cosaxuexx均可。