tangent
Not Supported
p
=
-
x
±
x
x0
-
4
(
x1
)
(
x2
x3
-
y
)
2
(
-
g
x
2
x4
)
Search
Returned 94 matches (100 formulae, 76 docs)
Lookup 622.275 ms, Re-ranking 1530.751 ms
Found 1639172 tuple postings, 191749 formulae, 21922 documents
[ formulas ]
[ documents ]
[ documents-by-formula ]
p
=
-
x
±
x
2
-
4
(
-
g
x
2
2
v
2
)
(
-
g
x
2
2
v
2
-
y
)
2
(
-
g
x
2
2
v
2
)
Doc 1
0.9245, -16.0000, 22.0000, 2.1152
testing/wikipedia/v3/09833.html
f
′′
(
x
)
=
(
q
p
)
(
q
p
-
1
)
x
q
p
-
2
Doc 2
0.2979, -12.0000, 4.0000, 0.2979
testing/wikipedia/v3/00467.html
p
=
v
2
±
v
4
-
g
(
g
x
2
+
2
y
v
2
)
g
x
Doc 1
0.9245, -16.0000, 22.0000, 2.1152
testing/wikipedia/v3/09833.html
θ
=
arctan
(
v
2
±
v
4
-
g
(
g
x
2
+
2
y
v
2
)
g
x
)
Doc 1
0.9245, -16.0000, 22.0000, 2.1152
testing/wikipedia/v3/09833.html
θ
=
tan
-
1
(
v
2
±
v
4
-
g
(
g
x
2
+
2
y
v
2
)
g
x
)
Doc 1
0.9245, -16.0000, 22.0000, 2.1152
testing/wikipedia/v3/09833.html
z
=
1
2
(
x
2
+
y
2
)
(
1
a
2
-
1
b
2
)
+
x
y
(
1
a
2
+
1
b
2
)
Doc 3
0.2595, -26.0000, 4.0000, 0.2595
testing/wikipedia/v3/02322.html
(
1
y
)
(
1
x
)
Doc 4
0.2062, -2.0000, 3.0000, 0.4124
testing/wikipedia/v3/00687.html
(
1
x
)
(
1
y
)
Doc 4
0.2062, -2.0000, 3.0000, 0.4124
testing/wikipedia/v3/00687.html
(
a
m
n
)
=
(
a
m
)
(
a
n
)
Doc 6
0.2062, -8.0000, 3.0000, 0.2062
testing/wikipedia/v3/02166.html
(
a
n
m
)
=
(
a
n
)
(
a
m
)
Doc 5
0.2062, -8.0000, 3.0000, 0.2062
testing/wikipedia/v3/06302.html
D
1
=
(
h
1
-
1
γ
)
(
1
h
1
-
1
h
2
)
Doc 7
0.2062, -14.0000, 4.0000, 0.2062
testing/wikipedia/v3/27298.html
K
s
p
=
(
N
A
(
Δ
)
V
)
x
(
N
B
(
Δ
)
V
)
y
Doc 8
0.2062, -14.0000, 3.0000, 0.4124
testing/wikipedia/v3/13717.html
K
s
p
=
(
N
A
(
f
)
V
)
x
(
N
B
(
f
)
V
)
y
Doc 8
0.2062, -14.0000, 3.0000, 0.4124
testing/wikipedia/v3/13717.html
0
=
-
g
x
2
2
v
2
p
2
+
x
p
-
g
x
2
2
v
2
-
y
Doc 1
0.9245, -16.0000, 22.0000, 2.1152
testing/wikipedia/v3/09833.html
0
=
-
g
x
2
2
v
2
tan
2
θ
+
x
tan
θ
-
g
x
2
2
v
2
-
y
Doc 1
0.9245, -16.0000, 22.0000, 2.1152
testing/wikipedia/v3/09833.html
σ
x
x
=
-
μ
b
2
π
(
1
-
ν
)
y
(
3
x
2
+
y
2
)
(
x
2
+
y
2
)
2
Doc 9
0.2062, -24.0000, 4.0000, 0.4905
testing/wikipedia/v3/06599.html
B
n
∼
1
n
(
n
W
(
n
)
)
n
+
1
2
exp
(
n
W
(
n
)
-
n
-
1
)
.
Doc 10
0.2062, -24.0000, 3.0000, 0.2062
testing/wikipedia/v3/02890.html
S
≈
2
-
1.5382
Γ
(
3
2
)
2
(
Γ
(
5
2
)
-
Γ
(
3
2
)
)
≈
0.0854
Doc 11
0.1818, -22.0000, 3.0000, 0.1818
testing/wikipedia/v3/27473.html
tan
(
arccsc
x
)
=
1
x
2
-
1
Doc 12
0.1681, -7.0000, 3.0000, 0.5042
testing/wikipedia/v3/04392.html
sin
(
arcsec
x
)
=
x
2
-
1
x
Doc 12
0.1681, -7.0000, 3.0000, 0.5042
testing/wikipedia/v3/04392.html
cos
(
arccsc
x
)
=
x
2
-
1
x
Doc 12
0.1681, -7.0000, 3.0000, 0.5042
testing/wikipedia/v3/04392.html
(
arcosh
x
)
′
=
1
x
2
-
1
Doc 13
0.1681, -7.0000, 3.0000, 0.1681
testing/wikipedia/v3/16716.html
=
2
(
t
a
-
floor
(
1
2
+
t
a
)
)
Doc 14
0.1681, -11.0000, 3.0000, 0.1681
testing/wikipedia/v3/01650.html
(
∂
z
∂
x
)
y
=
-
(
∂
z
∂
y
)
x
(
∂
y
∂
x
)
z
Doc 15
0.1681, -18.0000, 3.0000, 0.1681
testing/wikipedia/v3/14685.html
j
2
(
x
)
=
(
3
x
2
-
1
)
sin
(
x
)
x
-
3
cos
(
x
)
x
2
Doc 16
0.1681, -20.0000, 3.0000, 0.2978
testing/wikipedia/v3/00134.html
|
x
-
1
2
(
a
c
+
b
d
)
|
=
1
2
(
b
d
-
a
c
)
Doc 17
0.1681, -21.0000, 3.0000, 0.1681
testing/wikipedia/v3/27724.html
E
I
d
4
w
d
x
4
-
3
2
E
A
(
d
w
d
x
)
2
(
d
2
w
d
x
2
)
=
q
(
x
)
Doc 18
0.1681, -29.0000, 3.0000, 0.1681
testing/wikipedia/v3/09923.html
f
(
x
)
=
2
β
α
2
Γ
(
α
2
)
x
α
-
1
exp
(
-
β
x
2
)
Doc 19
0.1519, -19.0000, 4.0000, 0.3725
testing/wikipedia/v3/12246.html
r
x
y
=
x
y
¯
-
x
¯
y
¯
(
x
2
¯
-
x
¯
2
)
(
y
2
¯
-
y
¯
2
)
Doc 20
0.1519, -20.0000, 4.0000, 0.2532
testing/wikipedia/v3/10770.html
f
=
v
2
(
ℓ
L
x
)
2
+
(
m
L
y
)
2
+
(
n
L
z
)
2
Doc 21
0.1519, -20.0000, 3.0000, 0.1519
testing/wikipedia/v3/12330.html
w
=
∑
i
(
x
i
-
x
¯
)
(
d
i
-
d
¯
)
∑
i
(
x
i
-
x
¯
)
2
Doc 22
0.1519, -20.0000, 3.0000, 0.1519
testing/wikipedia/v3/09141.html
S
2
=
2
m
[
m
(
2
)
-
x
¯
2
2
x
¯
]
2
=
m
(
d
~
-
1
)
2
2
Doc 23
0.1519, -21.0000, 1.0000, 0.1519
testing/wikipedia/v3/29923.html
f
(
x
;
k
)
=
2
1
-
k
2
x
k
-
1
e
-
x
2
2
Γ
(
k
2
)
Doc 24
0.1519, -22.0000, 5.0000, 0.1519
testing/wikipedia/v3/09559.html
(
δ
-
(
λ
d
)
1
-
(
λ
d
)
)
2
Doc 25
0.1422, -10.0000, 2.0000, 0.1422
testing/wikipedia/v3/27745.html
tan
A
=
(
(
-
∂
z
∂
y
)
(
∂
z
∂
x
)
)
Doc 26
0.1422, -13.0000, 3.0000, 0.1422
testing/wikipedia/v3/00438.html
d
y
d
x
=
-
4
x
3
4
y
=
-
x
3
y
Doc 27
0.1422, -14.0000, 3.0000, 0.1422
testing/wikipedia/v3/03420.html
P
(
x
)
(
1
-
x
)
(
1
-
x
2
)
⋯
(
1
-
x
n
)
Doc 28
0.1422, -14.0000, 3.0000, 0.1422
testing/wikipedia/v3/30312.html
P
4
2
(
x
)
=
15
2
(
7
x
2
-
1
)
(
1
-
x
2
)
Doc 30
0.1422, -16.0000, 3.0000, 0.1422
testing/wikipedia/v3/07434.html
(
d
y
d
x
)
2
=
(
y
2
-
1
)
(
1
-
k
2
-
y
2
)
Doc 29
0.1422, -16.0000, 3.0000, 0.1422
testing/wikipedia/v3/04901.html
∫
(
x
2
2
+
y
x
)
d
y
=
y
x
2
2
+
x
y
2
2
Doc 31
0.1422, -18.0000, 4.0000, 0.1422
testing/wikipedia/v3/04191.html
f
(
x
)
=
1
2
1
2
Γ
(
1
2
)
x
-
1
2
e
-
x
2
Doc 32
0.1422, -20.0000, 2.0000, 0.1422
testing/wikipedia/v3/24722.html
(
1
2
(
x
-
1
x
)
)
2
+
1
=
(
1
2
(
x
+
1
x
)
)
2
,
Doc 34
0.1422, -21.0000, 2.0000, 0.1422
testing/wikipedia/v3/00703.html
θ
=
arctan
(
x
2
+
y
2
z
)
=
arccos
(
z
x
2
+
y
2
+
z
2
)
Doc 33
0.1422, -21.0000, 2.0000, 0.2844
testing/wikipedia/v3/13693.html
F
(
x
)
=
Φ
(
x
-
μ
σ
)
=
1
2
[
1
+
erf
(
x
-
μ
σ
2
)
]
Doc 35
0.1422, -22.0000, 2.0000, 0.1422
testing/wikipedia/v3/00697.html
Q
(
x
)
=
1
2
-
1
2
erf
(
x
2
)
=
1
2
erfc
(
x
2
)
.
Doc 36
0.1422, -23.0000, 3.0000, 0.1422
testing/wikipedia/v3/02688.html
σ
y
y
=
μ
b
2
π
(
1
-
ν
)
y
(
x
2
-
y
2
)
(
x
2
+
y
2
)
2
Doc 9
0.2062, -24.0000, 4.0000, 0.4905
testing/wikipedia/v3/06599.html
τ
x
y
=
μ
b
2
π
(
1
-
ν
)
x
(
x
2
-
y
2
)
(
x
2
+
y
2
)
2
Doc 9
0.2062, -24.0000, 4.0000, 0.4905
testing/wikipedia/v3/06599.html
ϕ
=
arctan
(
y
x
)
=
arccos
(
x
x
2
+
y
2
)
=
arcsin
(
y
x
2
+
y
2
)
Doc 33
0.1422, -21.0000, 2.0000, 0.2844
testing/wikipedia/v3/13693.html
4
⋅
∫
0
1
(
x
2
-
x
6
)
1
6
d
x
=
Γ
(
1
6
)
⋅
Γ
(
1
3
)
3
π
≈
2.804
,
Doc 37
0.1422, -30.0000, 2.0000, 0.1422
testing/wikipedia/v3/13906.html
V
=
1
2
(
x
1
2
+
x
2
2
)
Doc 38
0.1297, -9.0000, 3.0000, 0.1297
testing/wikipedia/v3/04297.html
f
(
x
)
=
x
3
-
2
x
2
(
x
2
-
5
)
Doc 39
0.1297, -12.0000, 4.0000, 0.1297
testing/wikipedia/v3/04272.html
cos
(
x
2
)
=
±
1
2
(
1
+
cos
x
)
Doc 40
0.1297, -12.0000, 2.0000, 0.1297
testing/wikipedia/v3/02375.html
j
1
(
x
)
=
sin
(
x
)
x
2
-
cos
(
x
)
x
Doc 16
0.1681, -20.0000, 3.0000, 0.2978
testing/wikipedia/v3/00134.html
η
p
=
2
(
v
v
e
)
1
+
(
v
v
e
)
2
Doc 41
0.1297, -14.0000, 3.0000, 0.1297
testing/wikipedia/v3/00547.html
T
=
1
2
x
˙
2
=
1
2
(
∂
x
∂
t
)
2
Doc 43
0.1297, -14.0000, 3.0000, 0.1297
testing/wikipedia/v3/06354.html
R
2
(
x
)
=
x
2
-
4
x
+
1
(
x
+
1
)
2
Doc 42
0.1297, -14.0000, 3.0000, 0.1297
testing/wikipedia/v3/14701.html
e
𝛀
θ
2
=
cos
(
θ
2
)
+
𝛀
sin
(
θ
2
)
Doc 44
0.1297, -14.0000, 2.0000, 0.1297
testing/wikipedia/v3/06855.html
K
(
2
2
)
=
1
4
π
Γ
(
1
4
)
2
Doc 46
0.1297, -14.0000, 2.0000, 0.1297
testing/wikipedia/v3/00354.html
K
n
(
x
)
=
(
x
2
)
n
𝒦
n
(
x
2
4
)
.
Doc 45
0.1297, -14.0000, 2.0000, 0.1297
testing/wikipedia/v3/14448.html
(
J
0
3
f
)
(
x
)
=
-
x
-
x
2
2
-
x
3
3
Doc 47
0.1297, -16.0000, 2.0000, 0.1297
testing/wikipedia/v3/08705.html
f
(
x
)
=
1
+
2
(
1
x
+
x
x
2
-
4
x
+
8
)
Doc 48
0.1297, -17.0000, 3.0000, 0.2384
testing/wikipedia/v3/03370.html
a
2
=
2
x
-
2
x
-
2
x
2
-
2
x
+
3
2
Doc 49
0.1297, -17.0000, 2.0000, 0.1297
testing/wikipedia/v3/30289.html
y
=
R
(
2
(
x
L
)
-
K
′
(
x
L
)
2
2
-
K
′
)
Doc 52
0.1297, -18.0000, 3.0000, 0.1297
testing/wikipedia/v3/09114.html
d
d
x
(
1
g
(
x
)
)
=
-
g
′
(
x
)
(
g
(
x
)
)
2
Doc 50
0.1297, -18.0000, 3.0000, 0.2595
testing/wikipedia/v3/13099.html
=
1
θ
k
Γ
(
k
)
(
1
y
)
k
+
1
exp
(
-
1
θ
y
)
Doc 51
0.1297, -18.0000, 3.0000, 0.2595
testing/wikipedia/v3/09040.html
K
=
2
(
Γ
(
n
-
1
2
)
)
2
(
Γ
(
n
-
2
2
)
)
2
.
Doc 53
0.1297, -19.0000, 2.0000, 0.2595
testing/wikipedia/v3/26874.html
d
d
x
(
1
g
(
x
)
)
=
d
d
x
(
f
(
x
)
g
(
x
)
)
Doc 50
0.1297, -18.0000, 3.0000, 0.2595
testing/wikipedia/v3/13099.html
1
+
7
x
+
12
x
2
-
4
x
3
(
1
-
x
2
)
(
1
-
16
x
2
)
Doc 54
0.1297, -20.0000, 3.0000, 0.3323
testing/wikipedia/v3/24194.html
Φ
(
k
+
1
)
(
ω
)
=
1
2
H
(
ω
2
)
Φ
(
k
)
(
ω
2
)
Doc 56
0.1297, -20.0000, 2.0000, 0.1297
testing/wikipedia/v3/17427.html
K
=
2
(
Γ
(
N
-
t
2
)
)
2
(
Γ
(
N
-
t
-
1
2
)
)
2
Doc 53
0.1297, -19.0000, 2.0000, 0.2595
testing/wikipedia/v3/26874.html
f
(
x
)
=
2
ω
ϕ
(
x
-
ξ
ω
)
Φ
(
α
(
x
-
ξ
ω
)
)
.
Doc 55
0.1297, -20.0000, 2.0000, 0.1297
testing/wikipedia/v3/21857.html
=
∂
(
1
2
(
t
j
-
y
j
)
2
)
∂
y
j
∂
y
j
∂
w
j
i
Doc 57
0.1297, -21.0000, 2.0000, 0.1297
testing/wikipedia/v3/07989.html
=
1
θ
k
Γ
(
k
)
(
1
y
)
k
-
1
exp
(
-
1
θ
y
)
1
y
2
Doc 51
0.1297, -18.0000, 3.0000, 0.2595
testing/wikipedia/v3/09040.html
f
(
x
)
=
1
2
k
/
2
Γ
(
k
/
2
)
x
k
2
-
1
exp
(
-
x
2
)
Doc 19
0.1519, -19.0000, 4.0000, 0.3725
testing/wikipedia/v3/12246.html
θ
=
tan
-
1
(
(
x
1
-
x
2
)
2
+
(
y
1
-
y
2
)
2
z
1
-
z
2
)
Doc 58
0.1297, -24.0000, 2.0000, 0.1297
testing/wikipedia/v3/23272.html
f
(
x
)
=
1
2
∫
ℝ
n
(
x
-
y
|
x
-
y
|
+
y
|
y
|
)
d
μ
(
y
)
Doc 59
0.1297, -24.0000, 2.0000, 0.1297
testing/wikipedia/v3/26239.html
∫
0
∞
x
n
e
-
a
x
2
d
x
=
Γ
(
(
n
+
1
)
2
)
2
a
(
n
+
1
)
2
Doc 61
0.1297, -26.0000, 3.0000, 0.1297
testing/wikipedia/v3/05600.html
π
x
2
6
-
3
x
2
-
(
x
2
)
2
2
+
x
2
-
(
x
2
)
2
2
Doc 60
0.1297, -26.0000, 3.0000, 0.1297
testing/wikipedia/v3/00025.html
v
a
r
[
log
(
t
a
)
]
=
(
s
a
2
t
a
2
+
(
x
a
-
x
¯
t
a
)
2
-
1
)
n
Doc 62
0.1297, -28.0000, 2.0000, 0.1297
testing/wikipedia/v3/00627.html
f
(
x
)
=
1
(
x
-
1
)
(
x
2
+
x
+
1
)
Doc 48
0.1297, -17.0000, 3.0000, 0.2384
testing/wikipedia/v3/03370.html
α
(
x
)
=
x
+
x
2
+
4
2
,
β
(
x
)
=
x
-
x
2
+
4
2
Doc 63
0.1087, -22.0000, 4.0000, 0.1087
testing/wikipedia/v3/05130.html
1
-
(
x
x
i
)
k
x
-
x
i
Doc 64
0.1013, -9.0000, 2.0000, 0.1013
testing/wikipedia/v3/01593.html
r
x
y
=
x
y
¯
(
x
2
¯
)
(
y
2
¯
)
Doc 20
0.1519, -20.0000, 4.0000, 0.2532
testing/wikipedia/v3/10770.html
1
+
7
x
(
1
-
x
2
)
(
1
-
16
x
2
)
Doc 54
0.1297, -20.0000, 3.0000, 0.3323
testing/wikipedia/v3/24194.html
f
(
i
)
i
=
1
2
+
O
(
log
log
i
i
)
Doc 65
0.1013, -14.0000, 1.0000, 0.1013
testing/wikipedia/v3/25357.html
v
=
x
-
x
¯
h
(
x
)
;
w
=
y
-
y
¯
h
(
y
)
Doc 66
0.1013, -17.0000, 3.0000, 0.1013
testing/wikipedia/v3/09762.html
p
=
∂
g
∂
z
(
∂
g
∂
x
)
2
+
(
∂
g
∂
y
)
2
Doc 67
0.1013, -20.0000, 3.0000, 0.1013
testing/wikipedia/v3/25915.html
(
1
+
2
x
)
(
1
+
5
x
-
16
x
4
)
(
1
-
x
2
)
(
1
-
16
x
2
)
Doc 54
0.1297, -20.0000, 3.0000, 0.3323
testing/wikipedia/v3/24194.html
d
(
d
(
d
y
d
x
)
d
x
)
d
x
=
(
d
d
x
)
3
(
f
(
x
)
)
Doc 68
0.1013, -22.0000, 2.0000, 0.1013
testing/wikipedia/v3/16694.html
b
3
=
3
y
2
-
y
1
(
x
2
-
x
1
)
2
Doc 69
0.0909, -14.0000, 1.0000, 0.0909
testing/wikipedia/v3/05524.html
d
(
d
(
d
(
f
(
x
)
)
d
x
)
d
x
)
d
x
,
Doc 70
0.0909, -16.0000, 2.0000, 0.0909
testing/wikipedia/v3/04654.html
1
(
R
-
x
)
2
+
1
(
R
+
x
)
2
=
1
r
2
Doc 71
0.0909, -17.0000, 1.0000, 0.0909
testing/wikipedia/v3/17918.html
r
=
z
(
1
+
(
x
-
x
′
)
2
+
y
′
2
z
2
)
1
2
Doc 72
0.0909, -19.0000, 1.0000, 0.1818
testing/wikipedia/v3/16497.html
x
(
2
x
2
+
y
2
)
y
(
a
2
-
x
2
)
=
d
y
d
x
Doc 73
0.0909, -19.0000, 1.0000, 0.0909
testing/wikipedia/v3/07344.html
r
≈
z
(
1
+
1
2
(
x
-
x
′
)
2
+
y
′
2
z
2
)
Doc 72
0.0909, -19.0000, 1.0000, 0.1818
testing/wikipedia/v3/16497.html
f
y
=
y
0
-
y
(
x
0
-
x
)
2
+
(
y
0
-
y
)
2
(
20
)
Doc 74
0.0909, -21.0000, 2.0000, 0.1818
testing/wikipedia/v3/23312.html
f
x
=
x
0
-
x
(
x
0
-
x
)
2
+
(
y
0
-
y
)
2
(
19
)
Doc 74
0.0909, -21.0000, 2.0000, 0.1818
testing/wikipedia/v3/23312.html
F
(
x
)
=
2
π
arcsin
(
x
)
=
arcsin
(
2
x
-
1
)
π
+
1
2
Doc 76
0.0909, -21.0000, 2.0000, 0.0909
testing/wikipedia/v3/25332.html
d
s
2
=
4
(
d
x
2
+
d
y
2
)
(
1
-
x
2
-
y
2
)
2
.
Doc 75
0.0909, -21.0000, 2.0000, 0.0909
testing/wikipedia/v3/21607.html
f
(
x
)
=
2
2
k
/
2
Γ
(
k
/
2
)
x
k
-
1
exp
(
-
x
2
2
)
Doc 19
0.1519, -19.0000, 4.0000, 0.3725
testing/wikipedia/v3/12246.html