()()()()()()()(
)(
)()()1
222
2
()'0
()'()'ln '1
(log )'ln 1ln '(sin )'cos cos 'sin tan 'sec cot 'csc sec 'sec tan csc 'csc cot arcsin 'arccos '1arctan '11cot '1a a x x x x
a c x ax a a a
e e x x a
x x
x x
x x
x x
x x
x x x
x x x
x x x x arc x x -========-==-==-=
==+-=+ 导数运算法则
()()()()()()()()()()()()()()()()()()()2'''''''''u x v x u x v x u x v x u x v x u x v x v x u x v x u x v x u x u x ±=±=+⎛⎫-= ⎪ ⎪⎡⎤⎝⎭⎣⎦
1220
ln 1ln 1log ln sin cos cos sin tan sec cot csc sec sec tan csc csc cot arcsin arccos 1arctan 1arc cot u u x x x x a dc dx ux dx
de e dx
da a adx
d x dx x
d x dx x a
d x xdx
d x xdx
d x xdx
d x xdx
d x x xdx
d x x xdx
d x dx d x dx d x dx x
d x -========-==-==-=
==+-=211dx x +
微分的四则运算：
()()2()0d u v du dv
d uv udv vdu
v udv vdu d u u u ±=±=+-⎛⎫=≠ ⎪⎝⎭
基本积分表
(
)122;
1,1;1
1ln ;
;
ln ;sin cos ;cos sin ;sec tan ;csc cot ;sec tan sec ;csc cot csc ;arcsin arccos u u x
x x x kdx kx C x dx x C u u dx x C x a a dx C a e dx e C xdx x C xdx x C xdx x C xdx x C x xdx x C x xdx x C x C x C +=+=+≠-+=+=+=+=-+=+=+=-+=+=-+=+=-+⎰⎰⎰⎰⎰
⎰⎰⎰⎰⎰⎰2;arctan cot ;1;.dx x C arc x C x shxdx chx C chxdx shx C =+=-++=+=+⎰⎰⎰
