Formulario
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FORMULARIO BSICO CLCULO DIFERENCIAL E INTEGRAL
DERIVADAS INTEGRALES INTEGRACIN POR PARTES
ALGEBRAICAS ALGEBRAICAS, EXPONENCIALES Y LOGARTMICAS Escoger u y dv. Siempre en dv debe ir dx.
u dv = u v v du
1 radin = 57.3
VRTICE DE UNA PARBOLA
V b 4 ac b2
2a 4a
FRMULA GRAL. ECUACIONES DE
SEGUNDO GRADO
X = b b2 4ac
2 a
PROPIEDADES DE LOGARITMOS log A + log B = log A B
log A log B = log A B
log A n
= n log A
d c = 0
dx
d x = 1
dx
d ( u + v w ) = d u + d v d w dx dx dx dx
d ( c u ) = c d u
dx dx
d ( u v ) = u d v + v d u
dx dx dx
d u n = n u
n 1 d u
dx dx
d u = d u
dx c dx
c
v d u u d v d u = dx dx
dx v v 2
d u
d u = dx
dx 2 u
EXPONENTES Y LOGARITMOS d ln u = 1 d u
dx u dx
d log u = 1 log e d u
dx u dx
d e u = e
u d u
dx dx
d a u = a
u ln a d u
dx dx
d uv = v u
v 1 d u + u
v ln u d v
dx dx dx
TRIGONOMTRICAS
d Sen u = Cos u d u
dx dx
d Cos u = Sen u d u dx dx
d Tg u = Sec2 u d u
dx dx
d Ctg u = Csc 2
u d u
dx dx
d Sec u = Sec u Tg u d u
dx dx
d Csc u = Csc u Ctg u d u dx dx
d arc Sen u = d u / dx
dx 1 u 2
d arc Cos u = d u / dx dx 1 u
2
d arc Tg u = d u / dx
dx 1 + u 2
d arc Ctg u = d u / dx dx 1 + u
2
d arc Sec u = d u/dx
dx u u 2 1
d arc Csc u = d u / dx
dx u u 2 1
d arc vers u = du / dx
dx 2u u 2
du = u + c
c du = c du
( du + dv dw ) = du + dv dw
u n du = u
n + 1 + c
n + 1
du = ln u + c
u
e u du = e
u + c
a u du = a
u + c
ln a
ln u du = u ln ( u 1 )
u au du = e
u ( u 1 )
TRIGONOMTRICAS Sen u du = Cos u + c
Cos u du = Sen u + c
Tg u du = ln ( Sec u ) = ln ( Cos u ) + c
Ctg u du = ln ( Sen u ) + c
Sec u du = ln ( Sec u + Tg u ) + c Csc u du = ln ( Csc u Ctg u ) + c
Sec2 u du = Tg u + c
Csc 2 u du = Ctg u + c
Sec u Tg u du = Sec u + c
Csc u Ctg u du = Csc u + c
du = 1 arctg u + c
u2 + a
2 a a
du = 1 ln u a + c u
2 a
2 2a u + a
du = 1 ln a + u + c
a2 u
2 2a a u
du = arc Sen u + c a
2 u
2 a
du = ln u + u2
a2 + c
u
2 a
2
a2 u
2 du = 1 u a
2 u
2 +
2
a2 arcSen u + c
2 a
u2
a2 du = 1 u
u
2 a
2
2
a2 ln u + u
2 a
2 + c
2
du = 1 arc Sec u + c
a a
u u2 a
2
FUNCIONES TRIGONOMTRICAS
Sen x = 1 = Cos x = Tg x
Csc x Ctg x Sec x
Cos x = 1 = Ctg x = Sen x
Sec x Csc x Tg x
Tg x = Sen x = Sec x = 1
Cos x Csc x Ctg x
Ctg x = Cos x = Csc x = 1
Sen x Sec x Tg x
Sec x = 1 = Tg x = Csc x
Cos x Sen x Ctg x
Csc x = 1 = Sec x = Ctg x
Sen x Tg x Cos x
Sen2 x + Cos
2 x = 1
Ctg2 x = Csc
2 x 1
Tg 2x = Sec
2 x 1
Sen
2 x = Cos 2x
Cos2 x = + Cos 2x
Sen ( A + B ) = Sen A Cos B + Cos A Sen B
Sen ( A B ) = Sen A Cos B Sen B Cos A
Cos ( A + B ) = Cos A Cos B Sen A Sen B
Cos ( A B ) = Cos A Cos B + Sen A Sen B
Tg ( A + B ) = Tg A + Tg B
1 Tg A Tg B Tg ( A B ) = Tg A Tg B 1 + Tg A Tg B
Sen 2x = 2 Sen x Cos x
Cos 2x = Cos2 x Sen
2 x
Tg 2x = 2 Tg x
1 Tg2 x