formulario

VII.IV.

Formularios

VII.IV.

Formularios

Fórmulas de derivación
Sean f (x), u = u(x), v = v(x) funciones y c una constante se tiene,

(1)

(13) f (x) = sen u

f (x) = c
f (x) = 0(2)

f (x) = x
f (x) = 1

(3)

f (x) = xn
f (x) = n · xn−1

(4)

f (x) = u + v
f (x) = u + v

(5)

f (x) = u · v
f (x) = u · v + v · u

(6)

u
v
v·u −u·v
f (x) =
v2
f (x)=

(7)

f (x) = un

(8)

f (x) = n · un−1 · u
√
f (x) = u
u
f (x) = √
2 u

(9)

(14) f (x) = cos u
f (x) = −sen u · u
(15) f (x) = tan u
f (x) = sec2 u · u
(16) f (x) = cot u
f(x) = − csc2 u · u
(17) f (x) = sec u
f (x) = sec u tan u · u
(18) f (x) = csc u
f (x) = − csc u cot u · u
(19) f (x) = arcsen u
f (x) = √

f (x) = e

f (x) = e · u
(10) f (x) = au
f (x) =au ln a · u
(11) f (x) = ln |u|
u
f (x) =
u
(12) f (x) = loga |u|
f (x) =

u
u ln a

u
1 − u2

(20) f (x) = arc cos u
f (x) = √

−u
1 − u2

(21) f (x) = arctan u

u
u

32

f(x) = cos u · u

f (x) =

u
1 + u2

(22) f (x) = arccot u
f (x) =

−u
1 + u2

(23) f (x) = arcsec u
u
f (x) = √
u u2 − 1
(24) f (x) = arccsc u
−u
f (x) = √
u u2 − 1
Lic. LucíaMarisol Valdés González

VII. Evidencias de aprendizaje

Identidades trigonométricas
– Fundamentales

(1)

sen x csc x = 1

(5)

(2)

cos x sec x = 1

(6)

cos x
sen x
sen2 x +cos2 x = 1

(3)

tan x cot x = 1
sen x
tan x =
cos x

(7)

1 + tan2 x = sec2 x

(8)

1 + cot2 x = csc2 x

(4)

cot x =

– Para sumas y diferencias

(9)

sen(x + y) = senx cos y +cos xseny

(13) tan(x + y) =

tan x + tan y
1 − tan x tan y

(14) tan(x − y) =

tan x − tan y
1 + tan x tan y

(10) cos(x + y) = cos x cos x − senxsenx
(11) sen(x − y) = senx cos y − cosxseny
(12) cos(x − y) = cos x cos x + senxsenx

– Para múltiplos y fracciones

(15) sen2x = 2senx cos x

(22)

(16) cos 2x = 2 cos2 x − sen2 x
(17) cos 2x = 1 − sen2 x

tan2 x =

(23)...