FORMULARIO BÁSICO CÁLCULO DIFERENCIAL E INTEGRAL
DERIVADAS
INTEGRALES
INTEGRACIÓN POR PARTES
ALGEBRAICAS
ALGEBRAICAS, EXPONENCIALES Y LOGARÍTMICAS
Escoger u y dv. Siempre en dv debe ir dx.
u dv = u v – v du
1 radián = 57.3°
VÉRTICE DE UNA PARÁBOLA
V – b 4 ac – b2
2a 4a
FÓRMULA 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 + uv ln u d v
dx dx dx
TRIGONOMÉTRICAS
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 = eu ( u – 1 )
TRIGONOMÉTRICAS
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 + a2 a a
du = 1 ln u – a + c
u2 – a2 2a u + a
du = 1 ln a + u + c
a2 – u2 2a a – u
du = arc Sen u + c
a2 – u2 a
du = ln u + u2 ± a2 + c
u2 ± a2
a2 – u2 du = 1 u a2 – u2 +
2
a2 arcSen u + c
2 a
u2 ± a2 du = 1 u u2 ± a2 ±
2
a2 ln u + u2 ± a2 + c
2
du = 1 arc Sec u + c
a a
u u2 – a2
FUNCIONES TRIGONOMÉTRICAS
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 + Cos2 x = 1
Ctg2 x = Csc2 x – 1
Tg 2x = Sec2 x – 1
Sen2 x = ½ – ½ Cos 2x
Cos2 x = ½ + ½ 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 – Sen2 x
Tg 2x = 2 Tg x
1 – Tg2 x
