Universidad

F O R M U L A R I O DE D E R I V A C I O N.
FUNCIONES ALGEBRAICAS

FUNCIÓN Nombre de la Función DERIVADA
f(x) = c Función Constante f '(x) = 0

f(x) = x Función Identidad f '(x) = 1

f(x) = xn Potencia de Identidad f '(x) = n xn-1 n(R

f(x) = u + v - w Suma de Funciones f '(x) = u' + v' - w'

f(x) = c v Constante por Función f '(x) = c v'

f(x) = u vProducto de Funciones f '(x) = u v' + v u'

f(x) = vn Potencia de Función f '(x) = n vn-1 v'

f(x) = u Cociente de Funciones f '(x) = v u' - uv'
v v2

f(x) = c Constante entre función f ’(x) = - c v’
v v2

[pic] Irracional [pic]
con u, v, w cualquier función algebraica.

F O R M U L A R I O DE D E R I V A C I O N.FUNCIONES CIRCULARES

FUNCIÓN Nombre de la Función DERIVADA
f(x) = sen u SENO f '(x) = cos u u'
f(x) = cos u COSENO f '(x) = - sen u u'
f(x) = tan u TANGENTE f '(x) = sec2 u u'
f(x) = ctg u COTANGENTE f '(x) = - csc2 u u'
f(x) = sec u SECANTE f '(x) = sec u tan u u'
f(x) = csc u COSECANTE f '(x) = - csc u ctg u u'

F O R M U L A R I O DE D E R IV A C I O N.
FUNCIONES CIRCULARES INVERSAS

FUNCIÓN Nombre de la Función DERIVADA
f(x) = ang sen u INVERSA DE SENO [pic]

f(x) = ang cos u INVERSA DE COSENO [pic]
f(x) = ang tan u INVERSA DE TANGENTE [pic]

f(x) = ang ctg u INVERSA DE COTANGENTE [pic]

f(x) = ang sec u INVERSA DE SECANTE [pic]

f(x) = ang csc u INVERSA DE COSECANTE [pic]

IGUALDADESTRIGONOMETRICAS
Relaciones Fundamentales: Sumas y Diferencias de Ángulos:
sen2 ( + cos2 ( = 1 sen( ((( ) = sen ( cos ( ( cos ( sen(
1+ tan2 ( = 1 cos(((( ) = cos ( cos ([pic]sen ( sen(
cos2( tan (((( ) = tan ( ( tan(
tan ( ctg ( = 1 1(-+)tan ( tan(
1+ ctg2 ( = 1 ctg(((( ) = ctg ( ctg ((-+) 1
sen2( ctg ( ( ctg(
Operaciones:sen ( + sen ( = 2sen ( + ( cos ( - ( sen ( cos ( = ½ sen( ( + ( )+ ½ sen( ( - ( )
2 2 cos ( cos ( = ½ cos( ( + () + ½ cos( ( - ( )
sen ( - sen ( = 2 cos ( + ( sen ( - ( sen ( sen ( = ½ cos( ( - ( ) - ½ cos( ( + ( )
2 2 tan ( tan ( = tan ( + tan( = - tan ( - tan(
cos ( + cos ( = 2 cos ( + ( cos ( - ( ctg ( + ctg( ctg ( - ctg(
2 2 ctg ( ctg ( =ctg ( + ctg ( = - ctg ( - ctg(
cos ( - cos ( = -2 sen ( + ( sen ( - ( tan ( + tan( tan ( - tan(
2 2 ctg ( tan ( = ctg ( + tan ( = - ctg ( - tan(
tan ( ( tan ( = sen( ( + ( ) tan ( + ctg( tan ( - ctg(
cos ( cos(
ctg ( ( ctg ( = sen( ((( )
sen ( sen(

FORMULARIO DE INTEGRACIÓN

( (du + dv - d() = ( du + ( dv - ( d(

( a du = a ( du

( dx = x + c

( un du =u n+1 + c
n + 1

( du = ln u + c = ln u + ln c = ln cu
u

( au du = au + c
ln a

( eu du = eu + c

( sen u du = -cos u + c

( cos u du = sen u + c

( sec2 u du = tg u +c

( csc2 u du = - ctg u + c

( sec u tg u du = sec u + c

( csc u ctg u du = - csc u + c

( tg u du = - ln cos u + c = ln sec 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

( du = 1 ang tg 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

[pic]


PROPIEDADES
Si u y v son números positivos cualesquiera, entonces se cumple que:
a) Ln(1) = 0
b) Ln(u v) = Ln(u) + Ln (v)
c) Ln(1/u) = -Ln(u)
d) Ln(u / v)= Ln(u) - Ln(v)
e) Ln(ur ) = r Ln(u)


|Función Logaritmo Natural Ln |Función Logaritmo Vulgar logb |
|Ln (1) = 0 |logb (1) = 0 |
|Ln (uv) = Ln (u) + Ln (v) |logb uv = logb u+ logb v |
|Ln (1/u) = - Ln (u)...