This document contains formulas for calculus, trigonometric functions, and their inverses. It includes formulas for: - Differentiation and integration of polynomials using the power, product, and quotient rules. - Trigonometric identities for sums and differences of sines, cosines, tangents, cotangents, secants and cosecants. - Graphs of trigonometric functions and their inverses over their domains. - Absolute value definitions. - Sum and difference formulas for trigonometric functions of angles.

1. Fórmulas de Cálculo Diferencial e Integral (Página 1 de 3) http://www.geocities.com/calculusjrm/ Jesús Rubí M.
Fórmulas de ( a + b ) ⋅ ( a 2 − ab + b 2 ) = a 3 + b3 θ sin cos tg ctg sec csc Gráfica 4. Las funciones trigonométricas inversas
arcctg x , arcsec x , arccsc x : sin α + sin β = 2sin
1 1
(α + β ) ⋅ cos (α − β )
∞ ∞
( a + b ) ⋅ ( a3 − a 2 b + ab 2 − b3 ) = a 4 − b 4
0 0 1 0 1 2 2
Cálculo Diferencial 30 12 3 2 1 3 3 2 3 2 4 1 1
sin α − sin β = 2 sin (α − β ) ⋅ cos (α + β )
( a + b ) ⋅ ( a 4 − a 3b + a 2 b 2 − ab3 + b 4 ) = a 5 + b5
e Integral VER.6.8 45 1 2 1 2 1 1 2 2 3
2 2
( a + b ) ⋅ ( a5 − a 4 b + a 3b 2 − a 2 b3 + ab 4 − b5 ) = a 6 − b 6
1 1
60 3 2 12 3 1 3 2 2 3 cos α + cos β = 2 cos (α + β ) ⋅ cos (α − β )
Jesús Rubí Miranda (jesusrubim@yahoo.com) 90 1 0 ∞ 0 ∞ 1
2 2 2
http://www.geocities.com/calculusjrm/ ⎛ n ⎞ 1 1
cos α − cos β = −2 sin (α + β ) ⋅ sin (α − β )
( a + b ) ⋅ ⎜ ∑ ( −1) a n− k b k −1 ⎟ = a n + b n ∀ n ∈
k +1
⎡ π π⎤ 1
impar y = ∠ sin x y ∈ ⎢− , ⎥ 2 2
⎝ k =1 ⎠ ⎣ 2 2⎦
VALOR ABSOLUTO
sin (α ± β )
0
⎛ ⎞ y = ∠ cos x y ∈ [ 0, π ]
n
⎧a si a ≥ 0 ( a + b ) ⋅ ⎜ ∑ ( −1)
k +1
a n − k b k −1 ⎟ = a n − b n ∀ n ∈ par tg α ± tg β =
a =⎨ ⎝ k =1 ⎠
-1
arc ctg x cos α ⋅ cos β
⎩− a si a < 0 π π arc sec x
y = ∠ tg x y∈ − , arc csc x
1
SUMAS Y PRODUCTOS sin α ⋅ cos β = ⎡sin (α − β ) + sin (α + β ) ⎤
-2
a = −a 2 2
2⎣ ⎦
-5 0 5
n
a ≤ a y −a ≤ a a1 + a2 + + an = ∑ ak y = ∠ ctg x = ∠ tg
1
y ∈ 0, π IDENTIDADES TRIGONOMÉTRICAS 1
k =1 x sin α ⋅ sin β = ⎡cos (α − β ) − cos (α + β ) ⎤
sin θ + cos 2 θ = 1 2⎣ ⎦
2
a ≥0 y a =0 ⇔ a=0 n
∑ c = nc
1
y = ∠ sec x = ∠ cos y ∈ [ 0, π ] 1 + ctg 2 θ = csc 2 θ 1
n n
x cos α ⋅ cos β = ⎡cos (α − β ) + cos (α + β ) ⎤
∏a = ∏ ak 2⎣ ⎦
k =1
ab = a b ó tg 2 θ + 1 = sec 2 θ
k n n
1 ⎡ π π⎤
k =1 k =1
∑ ca = c ∑ ak y = ∠ csc x = ∠ sen y ∈ ⎢− , ⎥ tg α + tg β
⎣ 2 2⎦ sin ( −θ ) = − sin θ
k
n n k =1 k =1 x tg α ⋅ tg β =
a+b ≤ a + b ó ∑a ≤ ∑ ak n n n ctg α + ctg β
cos ( −θ ) = cos θ
k
k =1 k =1
∑ ( ak + bk ) = ∑ ak + ∑ bk Gráfica 1. Las funciones trigonométricas: sin x ,
FUNCIONES HIPERBÓLICAS
cos x , tg x :
tg ( −θ ) = − tg θ
k =1 k =1 k =1
EXPONENTES
ex − e− x
sinh x =
n
a p ⋅ a q = a p+q ∑(a
k =1
k − ak −1 ) = an − a0 2
sin (θ + 2π ) = sin θ 2
ap e x + e− x
= a p−q
1.5
n
n cos (θ + 2π ) = cos θ cosh x =
aq
∑ ⎡ a + ( k − 1) d ⎤ = 2 ⎡ 2a + ( n − 1) d ⎤
⎣ ⎦ ⎣ ⎦
1
tg (θ + 2π ) = tg θ
2
(a )
p q
=a pq k =1 0.5
tgh x =
sinh x e x − e − x
=
n
= (a + l ) sin (θ + π ) = − sin θ cosh x e x + e− x
(a ⋅b)
0
= a ⋅b
p p p
2 -0.5
cos (θ + π ) = − cos θ 1 e x + e− x
p n
1 − r n a − rl ctgh x = =
⎛a⎞ ap
⎜ ⎟ = p ∑ ar = a 1 − r = 1 − r
k −1 -1
tg (θ + π ) = tg θ tgh x e x − e − x
⎝b⎠ b k =1
-1.5 sen x
1 2
sin (θ + nπ ) = ( −1) sin θ sech x = =
cos x n
∑ k = 2 ( n2 + n )
n
1 tg x
a p/q = a p cosh x e x + e − x
q
-2
-8 -6 -4 -2 0 2 4 6 8
cos (θ + nπ ) = ( −1) cos θ
n
k =1
LOGARITMOS 1 2
csch x = =
∑ k 2 = 6 ( 2n3 + 3n2 + n )
n
1 Gráfica 2. Las funciones trigonométricas csc x ,
log a N = x ⇒ a x = N tg (θ + nπ ) = tg θ sinh x e x − e − x
sec x , ctg x :
log a MN = log a M + log a N k =1
sinh : →
sin ( nπ ) = 0
∑ k 3 = 4 ( n 4 + 2n3 + n 2 )
n
1
M 2.5
cosh : → [1, ∞
log a = log a M − log a N k =1 2 cos ( nπ ) = ( −1)
n
N tgh : → −1,1
∑ k 4 = 30 ( 6n5 + 15n4 + 10n3 − n ) tg ( nπ ) = 0
n
1 1.5
log a N r = r log a N 1 ctgh : − {0} → −∞ , −1 ∪ 1, ∞
k =1
⎛ 2n + 1 ⎞
π ⎟ = ( −1)
log b N ln N
→ 0 ,1]
n
+ ( 2n − 1) = n
0.5
log a N = = 1+ 3 + 5 + 2 sin ⎜ sech :
log b a ln a 0
⎝ 2 ⎠
n csch : − {0} → − {0}
n! = ∏ k ⎛ 2n + 1 ⎞
-0.5
log10 N = log N y log e N = ln N -1 cos ⎜ π⎟=0
ALGUNOS PRODUCTOS k =1
-1.5 ⎝ 2 ⎠ Gráfica 5. Las funciones hiperbólicas sinh x ,
a ⋅ ( c + d ) = ac + ad ⎛n⎞ n! csc x
⎛ 2n + 1 ⎞
⎜ ⎟= , k≤n cosh x , tgh x :
-2
π⎟=∞
sec x
⎝ k ⎠ ( n − k )!k !
ctg x tg ⎜
( a + b) ⋅ ( a − b) = a − b 2 2
-2.5
-8 -6 -4 -2 0 2 4 6 8 ⎝ 2 ⎠ 5
n
⎛n⎞ π⎞
4
( a + b ) ⋅ ( a + b ) = ( a + b ) = a 2 + 2ab + b 2 ( x + y ) = ∑ ⎜ ⎟ xn−k y k ⎛
n
2 Gráfica 3. Las funciones trigonométricas inversas
sin θ = cos ⎜ θ − ⎟ 3
k =0 ⎝ k ⎠ arcsin x , arccos x , arctg x : ⎝ 2⎠
( a − b ) ⋅ ( a − b ) = ( a − b ) = a 2 − 2ab + b 2
2
2
n! ⎛ π⎞
( x1 + x2 + + xk ) = ∑
1
x1n1 ⋅ x2 2 cos θ = sin ⎜ θ + ⎟
n
( x + b ) ⋅ ( x + d ) = x 2 + ( b + d ) x + bd
n
xknk 4
⎝ 2⎠ 0
n1 ! n2 ! nk !
( ax + b ) ⋅ ( cx + d ) = acx 2 + ( ad + bc ) x + bd
-1
sin (α ± β ) = sin α cos β ± cos α sin β
3
CONSTANTES -2
( a + b ) ⋅ ( c + d ) = ac + ad + bc + bd π = 3.14159265359… 2
cos (α ± β ) = cos α cos β ∓ sin α sin β -3
senh x
cosh x
tgh x
( a + b ) = a3 + 3a 2b + 3ab 2 + b3
3 e = 2.71828182846… 1
tg α ± tg β
-4
-5 0 5
TRIGONOMETRÍA tg (α ± β ) = FUNCIONES HIPERBÓLICAS INV
( a − b ) = a 3 − 3a 2b + 3ab 2 − b3
3 1 ∓ tg α tg β
( )
0
sen θ =
CO
cscθ =
1
sin 2θ = 2sin θ cos θ sinh −1 x = ln x + x 2 + 1 , ∀x ∈
( a + b + c ) = a 2 + b 2 + c 2 + 2ab + 2ac + 2bc
2
HIP sen θ
( )
-1
cos 2θ = cos 2 θ − sin 2 θ
arc sen x
cosh −1 x = ln x ± x 2 − 1 , x ≥ 1
arc cos x
( a − b ) ⋅ ( a + ab + b ) = a − b
CA 1 arc tg x
2 2 3 3
cosθ = secθ = -2
2 tg θ
cosθ
-3 -2 -1 0 1 2 3
HIP tg 2θ = 1 ⎛1+ x ⎞
( a − b ) ⋅ ( a 3 + a 2 b + ab 2 + b3 ) = a 4 − b 4 sen θ CO 1 1 − tg 2 θ tgh −1 x = ln ⎜ ⎟, x <1
tgθ = = ctgθ = 2 ⎝1− x ⎠
( a − b ) ⋅ ( a 4 + a 3b + a 2 b 2 + ab3 + b 4 ) = a 5 − b5 cosθ CA tgθ 1
sin 2 θ = (1 − cos 2θ ) 1 ⎛ x +1⎞
2 ctgh −1 x = ln ⎜ ⎟, x >1
⎛ n
⎞ π radianes=180 2 ⎝ x −1⎠
( a − b ) ⋅ ⎜ ∑ a n − k b k −1 ⎟ = a n − b n ∀n ∈ 1
cos 2 θ = (1 + cos 2θ )
⎝ k =1 ⎠ 2 ⎛ 1 ± 1 − x2 ⎞
1 − cos 2θ sech −1 x = ln ⎜ ⎟, 0 < x ≤ 1
tg 2 θ = ⎜ x ⎟
⎝ ⎠
HIP
CO 1 + cos 2θ
⎛1 x2 + 1 ⎞
csch −1 x = ln ⎜ + ⎟, x ≠ 0
θ ⎜x x ⎟
⎝ ⎠
CA

2. Fórmulas de Cálculo Diferencial e Integral (Página 2 de 3) http://www.geocities.com/calculusjrm/ Jesús Rubí M.
∫ tgh udu = ln cosh u
IDENTIDADES DE FUNCS HIP d dv du DERIVADA DE FUNCS HIPERBÓLICAS INTEGRALES DE FUNCS LOG & EXP
( uv ) = u + v
cosh 2 x − sinh 2 x = 1 d du
∫ e du = e
u u
dx dx dx sinh u = cosh u
1 − tgh 2 x = sech 2 x d dw dv du dx dx ∫ ctgh udu = ln sinh u
( uvw ) = uv + uw + vw au ⎧a > 0
∫ a du = ln a ⎨a ≠ 1 ∫ sech udu = ∠ tg ( sinh u )
u
dx dx dx dx d du
ctgh 2 x − 1 = csch 2 x cosh u = sinh u
⎩
d ⎛ u ⎞ v ( du dx ) − u ( dv dx ) dx dx
sinh ( − x ) = − sinh x ∫ csch udu = − ctgh ( cosh u )
−1
⎜ ⎟= d du au ⎛ 1 ⎞
dx ⎝ v ⎠ v2 tgh u = sech 2 u ∫ ua du = ln a ⋅ ⎜ u − ln a ⎟
u
cosh ( − x ) = cosh x dx dx ⎝ ⎠ 1
= ln tgh u
tgh ( − x ) = − tgh x
d n
dx
( u ) = nu dx
n −1 du
d
ctgh u = − csch 2 u
du
∫ ue du = e ( u − 1)
u u 2
dx dx INTEGRALES DE FRAC
sinh ( x ± y ) = sinh x cosh y ± cosh x sinh y dF dF du ∫ ln udu =u ln u − u = u ( ln u − 1)
= ⋅ (Regla de la Cadena) d
sech u = − sech u tgh u
du du 1 u
cosh ( x ± y ) = cosh x cosh y ± sinh x sinh y dx du dx dx dx 1 u ∫ u 2 + a 2 = a ∠ tg a
du 1 ∫ log udu =( u ln u − u ) = ( ln u − 1)
tgh x ± tgh y
a
= d du ln a ln a
tgh ( x ± y ) = csch u = − csch u ctgh u 1 u
dx dx du = − ∠ ctg
1 ± tgh x tgh y dx dx u2
∫ u log a udu = 4 ⋅ ( 2log a u − 1)
a a
dF dF du 1 u−a
sinh 2 x = 2sinh x cosh x DERIVADA DE FUNCS HIP INV
=
∫ u 2 − a 2 = 2a ln u + a ( u > a )
du 2 2
dx dx du d 1 du u2
cosh 2 x = cosh 2 x + sinh 2 x
dy dy dt f 2′ ( t ) ⎪ x = f1 ( t )
⎧
senh −1 u = ⋅
1 + u 2 dx ∫ u ln udu = 4 ( 2ln u − 1) 1 a+u
∫ a 2 − u 2 = 2a ln a − u ( u < a )
dx du 2 2
tgh 2 x =
2 tgh x = = donde ⎨
1 + tgh 2 x dx dx dt f1′( t ) ⎪ y = f2 (t )
⎩ d ±1 du ⎧+ si cosh -1u > 0
⎪ INTEGRALES DE FUNCS TRIGO
cosh −1 u = ⋅ , u >1 ⎨
1 DERIVADA DE FUNCS LOG & EXP dx u 2 − 1 dx ⎪− si cosh u < 0
⎩
-1
∫ sin udu = − cos u INTEGRALES CON
sinh 2 x = ( cosh 2 x − 1)
2 d
( ln u ) =
du dx 1 du
= ⋅
d
tgh −1 u =
1 du
⋅ , u <1 ∫ cos udu = sin u ∫
du
= ∠ sin
u
1 dx u u dx dx 1 − u 2 dx a2 − u2 a
cosh 2 x = ( cosh 2 x + 1) ∫ sec udu = tg u
2
d log e du d 1 du
2 ( log u ) = ⋅ −1
ctgh u = ⋅ , u >1 = −∠ cos
u
cosh 2 x − 1 1 − u 2 dx ∫ csc udu = − ctg u
2
dx u dx dx a
tgh 2 x =
cosh 2 x + 1 du ⎧− si sech −1 u > 0, u ∈ 0,1
( )
d log e du
( log a u ) = a ⋅ a > 0, a ≠ 1 d
sech −1 u =
∓1
⋅ ⎨
⎪
∫ sec u tg udu = sec u ∫
du
= ln u + u 2 ± a 2
dx u dx sech −1 u < 0, u ∈ 0,1 u 2 ± a2
tgh x =
sinh 2 x dx u 1 − u 2 dx ⎪ + si
⎩
cosh 2 x + 1
d u
( e ) = eu ⋅ du d 1 du ∫ csc u ctg udu = − csc u du1 u
dx dx csch −1 u = − ⋅ , u≠0 ∫ u a 2 ± u 2 = a ln a + a 2 ± u 2
e x = cosh x + sinh x dx u 1 + u 2 dx ∫ tg udu = − ln cos u = ln sec u
e − x = cosh x − sinh x
d u
( a ) = au ln a ⋅ du
∫ ctg udu = ln sin u
du 1 a
dx dx INTEGRALES DEFINIDAS, PROPIEDADES
∫ u u 2 − a 2 = a ∠ cos u
ax 2 + bx + c = 0
OTRAS d v
dx
( u ) = vu v−1 du + ln u ⋅ u v ⋅ dv
dx dx
Nota. Para todas las fórmulas de integración deberá
agregarse una constante arbitraria c (constante de ∫ sec udu = ln sec u + tg u 1 u
= ∠ sec
⇒ x=
−b ± b 2 − 4ac
DERIVADA DE FUNCIONES TRIGO integración).
∫ csc udu = ln csc u − ctg u a a
∫ { f ( x ) ± g ( x )} dx = ∫ f ( x ) dx ± ∫ g ( x ) dx
b b b
d du a2
2a ( sin u ) = cos u u 1 2 2 u 2
∫ a − u du = 2 a − u + 2 ∠ sen a
2 u
∫ sin udu =
− sin 2u
a a a 2
dx dx
b 2 − 4ac = discriminante
∫ cf ( x ) dx = c ⋅ ∫ f ( x ) dx c ∈
b b
2 4
( )
d du
( cos u ) = − sin u
2
u 2 a
exp (α ± i β ) = e α
( cos β ± i sin β ) si α , β ∈ a a
u 1 ∫ u ± a du = 2 u ± a ± 2 ln u + u ± a
2 2 2 2 2
∫ cos udu = 2 + 4 sin 2u
2
dx dx
∫ f ( x ) dx = ∫ f ( x ) dx + ∫ f ( x ) dx
b c b
LÍMITES d du
( tg u ) = sec2 u MÁS INTEGRALES
a a c
∫ tg udu = tg u − u
2
∫ f ( x ) dx = − ∫ f ( x ) dx
1 b a
lim (1 + x ) x = e = 2.71828... dx dx e au ( a sin bu − b cos bu )
∫e sin bu du =
au
udu = − ( ctg u + u )
x →0 a b
d
( ctg u ) = − csc2 u
du
∫ ctg
2
a 2 + b2
∫ f ( x ) dx = 0
x a
⎛ 1⎞ dx dx
lim ⎜1 + ⎟ = e a e au ( a cos bu + b sin bu )
x →∞
⎝ x⎠ d
( sec u ) = sec u tg u
du
m ⋅ ( b − a ) ≤ ∫ f ( x ) dx ≤ M ⋅ ( b − a )
b ∫ u sin udu = sin u − u cos u ∫e
au
cos bu du =
a2 + b2
sen x dx dx
∫ u cos udu = cos u + u sin u
a
=1
⇔ m ≤ f ( x ) ≤ M ∀x ∈ [ a, b ] , m, M ∈
lim 1 1
∫ sec u du = 2 sec u tg u + 2 ln sec u + tg u
3
x →0 d du
x
( csc u ) = − csc u ctg u INTEGRALES DE FUNCS TRIGO INV
1 − cos x dx dx
∫ f ( x ) dx ≤ ∫ g ( x ) dx
b b
lim =0 ALGUNAS SERIES
∫ ∠ sin udu = u∠ sin u + 1 − u
2
x →0 d du
( vers u ) = sen u
a a
x
⇔ f ( x ) ≤ g ( x ) ∀x ∈ [ a , b ] f '' ( x0 )( x − x0 )
2
ex −1 dx dx f ( x ) = f ( x0 ) + f ' ( x0 )( x − x0 ) +
=1 ∫ ∠ cos udu = u∠ cos u − 1 − u
2
lim 2!
∫ f ( x ) dx ≤ ∫ f ( x ) dx si a < b
x →0 x DERIV DE FUNCS TRIGO INVER b b
∫ ∠ tg udu = u∠ tg u − ln 1 + u f ( n ) ( x0 )( x − x0 )
n
x −1 d 1 du a a 2
lim =1 ( ∠ sin u ) = ⋅ INTEGRALES + + : Taylor
x →1 ln x dx 1 − u 2 dx n!
∫ ∠ ctg udu = u∠ ctg u + ln 1 + u
2
DERIVADAS d 1 du ∫ adx =ax f '' ( 0 ) x 2
( ∠ cos u ) = − f ( x ) = f (0) + f ' ( 0) x +
∫ ∠ sec udu = u∠ sec u − ln ( u + u )
⋅
f ( x + ∆x ) − f ( x ) ∆y 2
−1
∫ af ( x ) dx = a ∫ f ( x ) dx
df 1 − u 2 dx
Dx f ( x ) = dx 2!
= lim = lim
dx ∆x →0 ∆x ∆x → 0 ∆x
d 1 du = u∠ sec u − ∠ cosh u f ( n) ( 0 ) x n
d ( ∠ tg u ) = ⋅
∫ ( u ± v ± w ± ) dx = ∫ udx ± ∫ vdx ± ∫ wdx ± + + : Maclaurin
∫ ∠ csc udu = u∠ csc u + ln ( u + )
(c) = 0 dx 1 + u 2 dx
u2 − 1
n!
∫ udv = uv − ∫ vdu ( Integración por partes )
dx d 1 du x 2 x3 xn
d ( ∠ ctg u ) = − ⋅ ex = 1 + x + + + + +
( cx ) = c dx 1 + u 2 dx
u n+1
= u∠ csc u + ∠ cosh u 2! 3! n!
dx
du ⎧+ si u > 1 ∫ u du = n + 1 n ≠ −1
n
d 1 INTEGRALES DE FUNCS HIP x 3 x5 x 7 x 2 n −1
( ∠ sec u ) = ± ⋅ ⎨ sin x = x − + − + + ( −1)
n −1
d
( cx n ) = ncx n−1 dx u u 2 − 1 dx ⎩− si u < −1 du ∫ sinh udu = cosh u 3! 5! 7! ( 2n − 1)!
dx
du ⎧− si u > 1 ∫u = ln u
x 2 n− 2
d du dv dw
(u ± v ± w ± ) = ± ± ±
d
( ∠ csc u ) = ∓
1
⋅ ⎨ ∫ cosh udu = sinh u cos x = 1 −
x2 x4 x6
+ − + + ( −1)
n −1
dx dx dx dx dx u u 2 − 1 dx ⎩+ si u < −1 2! 4! 6! ( 2n − 2 ) !
∫ sech udu = tgh u
2
d du d 1 du x2 x3 x 4 n
( cu ) = c ( ∠ vers u ) = ⋅ ln (1 + x ) = x −
+ − + + ( −1)
n −1 x
∫ csch udu = − ctgh u
2
dx dx dx 2u − u 2 dx 2 3 4 n
2 n −1
x3 x 5 x 7
∫ sech u tgh udu = − sech u ∠ tg x = x − + −
3 5 7
+ + ( −1)
n −1 x
2n − 1
∫ csch u ctgh udu = − csch u

3. Fórmulas de Cálculo Diferencial e Integral (Página 3 de 3) http://www.geocities.com/calculusjrm/ Jesús Rubí M.
ALFABETO GRIEGO
Mayúscula Minúscula Nombre Equivalente
Romano
1 Α α Alfa A
2 Β β Beta B
3 Γ γ Gamma G
4 ∆ δ Delta D
5 Ε ε Epsilon E
6 Ζ ζ Zeta Z
7 Η η Eta H
8 Θ θ ϑ Teta Q
9 Ι ι Iota I
10 Κ κ Kappa K
11 Λ λ Lambda L
12 Μ µ Mu M
13 Ν ν Nu N
14 Ξ ξ Xi X
15 Ο ο Omicron O
16 Π π ϖ Pi P
17 Ρ ρ Rho R
18 Σ σ ς Sigma S
19 Τ τ Tau T
20 Υ υ Ipsilon U
21 Φ φ ϕ Phi F
22 Χ χ Ji C
23 Ψ ψ Psi Y
24 Ω ω Omega W
NOTACIÓN
sin Seno.
cos Coseno.
tg Tangente.
sec Secante.
csc Cosecante.
ctg Cotangente.
vers Verso seno.
arcsin θ = sin θ Arco seno de un ángulo θ .
u = f ( x)
sinh Seno hiperbólico.
cosh Coseno hiperbólico.
tgh Tangente hiperbólica.
ctgh Cotangente hiperbólica.
sech Secante hiperbólica.
csch Cosecante hiperbólica.
u, v, w Funciones de x , u = u ( x ) , v = v ( x ) .
Conjunto de los números reales.
= {…, −2, −1,0,1, 2,…} Conjunto de enteros.
Conjunto de números racionales.
c
Conjunto de números irracionales.
= {1, 2,3,…} Conjunto de números naturales.
Conjunto de números complejos.