formulario
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)...
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