Tabela de derivadas e integrais completa

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TABELA DE DERIVADAS
(01) y = c ( y ( = 0 
(02) y = x ( y ( = 1
(03) y = c.u ( y ( = c. u ( 
(04) y = u + v ( y (= u ( + v (
(05) y = u . v ( y (= v. u ( + u. v ( 
(06) y = u / v ( y ( = ( v.u ( - u v() / v2 
(07) y = u( ( y ( = ( u( -1.u (
(08) y = au ( y ( = au lna.u (
(09) y = eu ( y ( = eu.u (
(10) 
(11) y = ln u ( y ( = ( u (/ u)
(12) y = uv ( y ( = v. uv -1. u ( + uv. ln u. v (
(13) y = sen u ( y ( = cos u. u (
(14) y = cos u ( y ( = - sen u. u (
(15) y = tg u ( y ( = sec2 u. u (
(16) y = cotg u ( y ( = - cosec2 u. u (
(17) y = sec u ( y ( = sec u. tg u. u (
(18) y = cosec u ( y ( = - cosec u. cotg u. u (
(19) y = arc sen u ( y ( = u ( /
(20) y = arc cos u ( y ( = - u ( /
(21) y = arc tg u ( y ( = u ( / (1 + u2 )
(22) y = arc cotg u ( y ( = - u ( / (1 + u2 )
(23) y = arc sec u ( y ( = u ( /
(24) y = arc cosec u ( y ( = - u ( /
(25) y = senh u ( y ( = coshu. u (
(26) y = cosh u ( y ( = senh u. u (
(27) y = tgh u ( y ( = sech2 u. u (
(28) y = cotgh u ( y ( = - cosech2 u. u ( 
(29) y = sech u ( y ( = - sech u. tgh u. u ( 
(30) y = cosech u ( y ( = - cosech u. cotgh u. u ( 
(31) y = arg senh u ( y ( = u ( /
(32) y = arg cosh u ( y ( = u ( /
(33) y = arg tgh u ( y ( = u ( / (1 - u2 )
(34) y = arg cotgh u ( y ( = u ( / (1 - u2 )
(35) y = arg sech u ( y ( = - u ( /
(36) y = arg cosech u ( y ( = - u ( /
TABELA DE INTEGRAIS
(01)
(02)
(03)
(04)
(05)
(06)
(07)
(08)
(09)
(10)
(11)
(12)
(13)
(14)
(15)
(16)
(17)
(18)
(19)
(20)
(21)
(22)
(23)
(24)
(25)
(26) 
(27) 
FÓRMULAS DE RECORRÊNCIA
(01) 
(02) 
(03) 
(04) 
(05) 
(06) 
(07)
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IDENTIDADES TRIGONOMÉTRICAS
(1) sen2x + cos2x = 1 
 
(2) 1 + tg2x = sec2x 
(3) 1 + cotg2x = cosec2x 
(4) sen2x = ½ (1 – cos2x) 
(5) cos2x = ½ (1 + cos2x) 
(6) sen2x = 2senx cosx
(7) senx cosy = ½ [sen(x – y) + sen(x + y)]
(8) senx seny = ½ [cos(x – y) - cos(x + y)]
(9) cosx cosy = ½ [cos(x – y) + cos(x + y)]
(10) cos (a ( b) = cosa.cosb 
 sena.senb
(11) sen (a ( b) = sena.cosb ( senb.cosa
(12) tgx = senx / cosx
(13) cotgx = cosx / senx
(14) secx = 1 / cosx
(15) cosecx = 1 / senx
INTEGRAÇÃO POR SUBSTITUIÇÕES
 TRIGONOMÉTRICAS
	
 a 
u 
 
 
	
u = a sen (
du = a cos( d(
= a.cos(
	
 
u 
 
 
 a 
	
u = a tg (
du = a sec2 ( d(
= a.sec(
	
 
 u 
 
 a
	
u = a sec (
du = a sec ( tg ( d(
= a. tg (
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Prof º :Eduardo Duarte
Disciplina: Cálculo Diferencial e Integral
Professor: Eduardo Duarte	Página � PAGE \* MERGEFORMAT �1�
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