導(dǎo)數(shù)公式微分公式與積分公式比較

1、導(dǎo)數(shù)公式、微分公式和積分公式的比較(cr=o,d(C) = (f血二C(g)寸廠懐()一d(xA) = pH 1 <Lv d(Vx) = <Lv2 Jr<!(-) = Xxff= 1 嚴(yán)】+C(tTH 1),fZ + 1j-fc = ln x +C(x0)(/yFln (exy = ed(«A ) = #' In adx<l(ev) =eY dx j耳£lXdx =+C(LJ > 0, £2 1),嵐械二曠+C(logfl x)r=, lnxy = i,<l(logv) = -(Lvd(lnx)=cLrxlnnxxlna

2、X基本公式導(dǎo)數(shù)公式微分公式積分公式積分公式J cos xdx = sin x + C f sin xdx cos x + Cj tan xdx - - In cosjc| + C j cot xdx = In | sin x+C cscx<=J sinxsec= f = In secx+ tanx + C = In tan cos x基本三角函數(shù)公式導(dǎo)數(shù)公式(sin x)r = cos x ,(cos x)f = - sin x , (tanx)f = sec2 x.(cot x)' = -cscv, (secx)'= sec x tan x .(cscx/= -cscx

3、cot x ,微分公式<l(sin x) =cosx<Lvd(cos x) = - sin x(1a-d(tan x) = sec xdxd(cot x) = -esc2 xd,v d(secx) = sec xtanxiLv (l(CSCAf) = - esc x cot 龍 cLyx-In esc x-cot x + C = In tan +C 2+ U 4 J反三角函數(shù)公式導(dǎo)數(shù)公式微分公式積分公式(arcmin a:-Vl - A 2d(arsinx)二,ilvyjl-x2f 1 dx - arcsin x + C(或-arccos x + C) VI-X2(arccosx)

4、 -一!,Vl x2d(arccosA)-<LvVI-A 2(arctanx)f =冷,1 + x"<l(arctan.v)二一 dx1 + xx= arctan x + C - arc colx+ C)1 + xCarccotx)'=-.1 + x2dfarccot x) =<Lv1 + x其他積分公式J _dx = J sec2 xdx =tanx + CCOS XJdx = J esc2 xdx = cot 兀 + Ca2 _ x2dxdx x2 - a2a-xdxa - xdx2 , 2 a + xdx.兀 小二 arcsm 一 + C a+C= arctan 二+ C aaJ J/ _x2x 22 axa - xarcta nC22aIn x+ Jx2 士 a2 十 C1 Jx2 土 a2dx = Z Jx2 土 a2 + In x + %21 xex s