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