基本导数公式-CAL-FENGHAI.-(YICAI)-Company One1
基本导数公式
⑴()0c '= ⑵1x x μμμ-= ⑶()sin cos x x '=
⑷()cos sin x x '=- ⑸()2tan sec x x '= ⑹()2cot csc x x '=- ⑺()sec sec tan x x x '=⋅ ⑻()csc csc cot x x x '=-⋅
⑼()x x e e '= ⑽()ln x x a a a '= ⑾()1ln x x
'= ⑿()1log
ln x a x a '= ⒀()arcsin x '= ⒁()arccos x '=
微分公式与微分运算法则
⑴()0d c = ⑵()1d x x dx μμμ-= ⑶()sin cos d x xdx =
⑷()cos sin d x xdx =- ⑸()2tan sec d x xdx = ⑹()2cot csc d x xdx =- ⑺()sec sec tan d x x xdx =⋅ ⑻()csc csc cot d x x xdx =-⋅ ⑼()x x d e e dx = ⑽()ln x x d a a adx = ⑾()1ln d x dx x =
⑿()1log
ln x a d dx x a = ⒀()arcsin d x = ⒁()arccos d x = ⒂()21arctan 1d x dx x
=
+ ⒃()21arccot 1d x dx x =-+
微分运算法则 ⑴()d u v du dv ±=± ⑵()d cu cdu = ⑶()d uv vdu udv =+ ⑷2u vdu udv d v v -⎛⎫= ⎪⎝⎭
基本积分公式
⑴kdx kx c =+⎰ ⑵11x x dx c μμ
μ+=++⎰ ⑶ln dx x c x =+⎰ ⑷ln x
x
a a dx c a =+⎰ ⑸x x e dx e c =+⎰ ⑹cos sin xdx x c =+⎰ ⑺sin cos xdx x c =-+⎰
⑻
221sec tan cos dx xdx x c x ==+⎰⎰ ⑼221csc cot sin xdx x c x ==-+⎰⎰ ⑽21arctan 1dx x c x =++⎰
⑾
arcsin x c =+
分部积分法公式
⑴形如n ax x e dx ⎰，令n u x =，ax dv e dx =
形如sin n x xdx ⎰
令n u x =，sin dv xdx = 形如cos n x xdx ⎰
令n u x =，cos dv xdx = ⑵形如arctan n x xdx ⎰
，令arctan u x =，n dv x dx = 形如ln n x xdx ⎰，令ln u x =，n dv x dx = ⑶形如sin ax e xdx ⎰，cos ax e xdx ⎰令,sin ,cos ax
u e x x =均可。

第二换元积分法中的三角换元公式
sin x a t =tan x a t =sec x a t =。