Tabela de derivadas e Integrais

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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)
----------------------------------------------------------------------------
 Prof ª : Fátima Ahmad Rabah Abido
Disciplina: Cálculo Diferencial e Integral
Departamento de Engenharia, Arquitetura e Tecnologia
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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Nome:
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