1、導數公式:(tgx) sec x(ctgx)csc x(secx) secx tgx(cscx)cscx ctgx(ax)axl na(log a x) 1xl na基本積分表：tgxdx ctgxdx secxdx cscxdx dx 2a xdx 2x adx 2a xdx2a x高等數學公式In cosx CIn sinx CIn secx tgx CIn cscx ctgx C1x-arctg Caa1x aInC2ax a1a xInC2a a xarcs in仝 C aIn2sin xdxcosx22 a 'x22 a 'a2x2dxdxdxo三角函數的有理式積分:

2、2usin x 2, cosx1 u22u2，1 u(arcsin x)(arccos x)(arctgx)(arcctgx)dx2 cos xdx2-sin xxdxx2x22 ax2x22 ax21 a2 xn2o111x211x2sec2 xdx tgx C2csc xdx ctgx Csecx tgxdx secx Ccscx ctgxdx cscx Cxaxdx CIn ashxdx chx Cchxdx shx C2 2 In( x 、x a ) C2 2 v 7 x aIn2 a In( x22 a . 一In x22a . x arcs inC2x2 a2) C、x2 a2dx

3、2du1 u2x e ex2xxe e2shxx ex echxx ex ex2 1)雙曲正弦：shx雙曲余弦:chx 雙曲正切:thxarshx In (xsin x lim1x 0 xlim(1 -)x xarchx In (xx2 1)arthxllnl三角函數公式:誘導公式：sin()sinCOSCOSsinCOS()COSCOSsinsintg()汽tg1 tgtgCtg()CtgCtg1CtgCtg-和差角公式:sinsin2 si nCOS22sinsin2 cossin22-和差化積公式:COS COS 2 COSCOS2 2COSCOS2 si nsin22函數 角A、sin

4、COStgCtg-a-sin aCOS a-tg a-Ctg a90 °aCOs asin aCtg atg a90 + aCOs a-sin a-Ctg a-tg a180 °asin a-COS a-tg a-Ctg a180 °a-sin a-COS atg aCtg a270 ° a-COs a-sin aCtg atg a270 + a-COS asin a-Ctg a-tg a360 ° a-sin aCOS a-tg a-Ctg a360 + asin aCOS atg aCtg asin 22 sin coscos222 cos

5、ctg2ctg212ctgtg22tg2倍角公式:-半角公式:1 1 2si n22 cos2 sinsin33si ncos34 cos3tg33tg4si n33cos.3tg2sin 21 coscos 21 costg21cos1 cossin.1cossin1cosabc2Rsin Asin Bsi nC2-正弦定理ctg?1 cos1 cossinsin1 cos-余弦定理:c2a2b2 2ab cosC-反三角函數性質：arcs in x arccosxarctgx arcctgx22高階導數公式萊布尼茲(Leibniz )公式:(uv)(n)nC：u(n k)v(k)k 0u(n)v(n 1)n(n 1) (n 2)n(n 1) (n k 1) (n k) (k)(n)nu vu vuvuv2!k!中值定理與導數應用：拉格朗日中值定理