TABELA DE DERIVADAS

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 ln a . 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)

FRMULAS DE RECORRNCIA

(01)

(02)

(03)

(04)

(05)

(06)

(07)

IDENTIDADES TRIGONOMTRICAS

(1) sen2x + cos2x = 1

(2) 1 + tg2x = sec2x

(3) 1 + cotg2x = cosec2x

(4) sen2x = (1 cos2x)

(5) cos2x = (1 + cos2x)

(6) sen2x = 2senx cosx

(7) senx cosy = [sen(x y) + sen(x + y)]

(8) senx seny = [cos(x y) - cos(x + y)]

(9) cosx cosy = [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

INTEGRAO POR SUBSTITUIES

TRIGONOMTRICAS

a

u

u = a sen (du = a cos( d(

= a.cos(

u

a u = a tg (du = a sec2 ( d(

= a.sec(

u

au = a sec (du = a sec ( tg ( d(

= a. tg (

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