微积分公式表

数学考研资料-1-微积分公式表导数函数积分备注幂函数系0kCkx1xx—kx11kxk)1(kCxdxx2121xx1xlnCxdxx112211xxarctan211)(xarthxxxarthx11ln21221axaxaarctan122221111axaax221axaxaxaln21)11(21122axaxaax211xxarcsin211)(xarshx)1ln(2xxarshx221xaaxarcsin222111axaxa221xa)ln(22xax222111axaxa221ax22lnaxx11)(2xarchx)1ln(2xxarshx指数函数系指数函数xexexe)0(~1xxexaaxlnxaaaxlnaxxealn对数函数x1xlnxxxln)0(~)1ln(xxxaxln1xalogaxxxalnlogaxxalnlnlog数学考研资料-2-导数函数积分备注三角函数系三角函数xcosxsinxcos)0(~sinxxxxsinxcosxsin)0(21~cos12xxxx2secxtanxcoslnxxxcossintanx2cscxcotxsinlnxxxsincoscotxxtansecxsecxxtansecln)42tan(lnxxxtanseclnxxcos1secxxcotcscxcscxxcotcscln2tanlnxxxsin1cscx2secxtanxx22seccos1x2cscxcotxx22cscsin1xxtansecxsecxxcotcscxcsc反三角函数211xxarcsin21arcsinxxx211)(xarshx211xxarccos21arcsinxxx2arccosarcsinxx211xxarctan)1ln(21arctan2xxx211)(xarthx211xxarccot)1ln(21arctan2xxx2cotarctanxarcx双曲函数chxshxchx2xxeeshxshxchxshx2xxeechxxch21thxchxlnxxxxeeeechxshxthx