tangent
Not Supported
d
d
x
(
log
c
x
)
=
1
x
ln
c
,
c
>
0
,
c
≠
1
Search
Returned 94 matches (100 formulae, 76 docs)
Lookup 7.699 ms, Re-ranking 469.597 ms
Found 130692 tuple postings, 85656 formulae, 15492 documents
[ formulas ]
[ documents ]
[ documents-by-formula ]
d
d
x
(
log
c
x
)
=
1
x
ln
c
,
c
>
0
,
c
≠
1
Doc 1
1.0000, 0.0000, 22.0000, 2.6018
testing/wikipedia/v3/16716.html
d
d
x
(
ln
x
)
=
1
x
,
x
≠
0
Doc 1
1.0000, 0.0000, 22.0000, 2.6018
testing/wikipedia/v3/16716.html
d
d
x
(
ln
x
)
=
1
x
.
Doc 2
0.4878, -1.0000, 10.0000, 0.4878
testing/wikipedia/v3/06735.html
d
d
x
(
ln
|
x
|
)
=
1
x
.
Doc 3
0.4412, -3.0000, 9.0000, 0.6484
testing/wikipedia/v3/00699.html
d
d
x
(
x
)
=
1
x
x
=
1
Doc 4
0.3945, -4.0000, 9.0000, 0.3945
testing/wikipedia/v3/10330.html
d
d
x
(
ln
|
x
|
)
=
|
x
|
x
2
Doc 1
1.0000, 0.0000, 22.0000, 2.6018
testing/wikipedia/v3/16716.html
d
d
s
(
c
g
E
)
=
0
,
Doc 5
0.3673, -2.0000, 6.0000, 0.3673
testing/wikipedia/v3/22675.html
d
d
x
(
f
*
g
)
=
d
f
d
x
*
g
.
Doc 6
0.3673, -8.0000, 7.0000, 0.3673
testing/wikipedia/v3/00237.html
d
d
t
(
∂
L
∂
𝐪
˙
)
=
∂
L
∂
𝐪
,
Doc 7
0.3673, -9.0000, 7.0000, 0.3673
testing/wikipedia/v3/04933.html
d
d
x
(
c
a
x
)
=
c
a
x
ln
c
⋅
a
,
c
>
0
Doc 1
1.0000, 0.0000, 22.0000, 2.6018
testing/wikipedia/v3/16716.html
d
x
d
t
(
T
)
=
d
y
d
t
(
T
)
=
0
,
Doc 8
0.3478, -10.0000, 6.0000, 0.5078
testing/wikipedia/v3/01064.html
d
d
x
(
ρ
u
ϕ
)
=
d
d
x
(
d
ϕ
d
x
)
Doc 9
0.3478, -11.0000, 7.0000, 0.6489
testing/wikipedia/v3/30201.html
d
d
x
(
u
+
v
)
=
d
u
d
x
+
d
v
d
x
Doc 10
0.3478, -12.0000, 7.0000, 0.3478
testing/wikipedia/v3/02342.html
Doc 11
0.3478, -12.0000, 7.0000, 0.3478
testing/wikipedia/v3/02352.html
d
d
x
ln
(
x
)
=
1
x
,
x
>
0.
Doc 12
0.3200, -7.0000, 7.0000, 1.2900
testing/wikipedia/v3/00254.html
d
d
x
(
L
-
u
′
∂
L
∂
u
′
)
=
0
,
Doc 13
0.3200, -10.0000, 7.0000, 0.3200
testing/wikipedia/v3/22142.html
d
d
x
(
1
g
(
x
)
)
=
-
g
′
(
x
)
(
g
(
x
)
)
2
Doc 14
0.3200, -14.0000, 7.0000, 0.9411
testing/wikipedia/v3/13099.html
d
d
x
(
1
g
(
x
)
)
=
d
d
x
(
f
(
x
)
g
(
x
)
)
Doc 14
0.3200, -14.0000, 7.0000, 0.9411
testing/wikipedia/v3/13099.html
d
d
x
(
ρ
u
)
=
0
Doc 9
0.3478, -11.0000, 7.0000, 0.6489
testing/wikipedia/v3/30201.html
d
d
x
(
e
x
)
=
e
x
Doc 1
1.0000, 0.0000, 22.0000, 2.6018
testing/wikipedia/v3/16716.html
d
d
x
(
μ
y
)
=
μ
q
(
x
)
Doc 15
0.3011, -5.0000, 6.0000, 0.3011
testing/wikipedia/v3/00266.html
Doc 16
0.3011, -5.0000, 6.0000, 0.3011
testing/wikipedia/v3/10464.html
d
d
x
log
b
x
=
1
x
ln
b
,
Doc 17
0.3011, -7.0000, 6.0000, 0.5083
testing/wikipedia/v3/00594.html
d
d
x
(
1
x
3
+
4
x
)
=
-
3
x
2
-
4
(
x
3
+
4
x
)
2
.
Doc 14
0.3200, -14.0000, 7.0000, 0.9411
testing/wikipedia/v3/13099.html
d
d
t
(
p
ρ
γ
)
=
0
,
Doc 18
0.2878, -4.0000, 6.0000, 0.2878
testing/wikipedia/v3/01210.html
d
u
d
x
(
x
)
=
0
,
Doc 19
0.2724, -3.0000, 7.0000, 0.2724
testing/wikipedia/v3/01665.html
f
(
x
)
=
1
x
,
Doc 21
0.2542, -2.0000, 6.0000, 0.2542
testing/wikipedia/v3/04315.html
ϕ
(
x
)
=
1
x
,
Doc 20
0.2542, -2.0000, 6.0000, 0.5085
testing/wikipedia/v3/16444.html
ϕ
(
x
)
=
1
x
s
,
Doc 20
0.2542, -2.0000, 6.0000, 0.5085
testing/wikipedia/v3/16444.html
D
(
f
)
=
d
f
d
x
.
Doc 22
0.2542, -4.0000, 3.0000, 0.2542
testing/wikipedia/v3/07469.html
d
d
x
(
x
2
)
=
2
x
.
Doc 23
0.2542, -5.0000, 6.0000, 0.2542
testing/wikipedia/v3/00145.html
d
k
f
d
x
k
(
x
)
=
0
Doc 24
0.2542, -5.0000, 6.0000, 0.2542
testing/wikipedia/v3/23979.html
d
y
d
x
(
1
+
x
2
)
=
1
Doc 25
0.2542, -6.0000, 6.0000, 0.8285
testing/wikipedia/v3/17871.html
δ
(
x
)
=
d
H
(
x
)
d
x
,
Doc 26
0.2542, -6.0000, 4.0000, 0.2542
testing/wikipedia/v3/03301.html
v
(
k
)
=
1
ℏ
d
ℰ
d
k
Doc 27
0.2542, -6.0000, 4.0000, 0.2542
testing/wikipedia/v3/17508.html
d
y
d
x
(
1
+
tan
2
y
)
=
1
Doc 25
0.2542, -6.0000, 6.0000, 0.8285
testing/wikipedia/v3/17871.html
d
y
d
x
(
5
y
4
-
1
)
=
1
Doc 28
0.2542, -7.0000, 6.0000, 0.4297
testing/wikipedia/v3/03420.html
v
s
(
t
)
=
d
x
s
(
t
)
d
t
,
Doc 29
0.2542, -8.0000, 4.0000, 0.2542
testing/wikipedia/v3/01147.html
d
d
x
log
a
(
x
)
=
1
x
ln
(
a
)
.
Doc 12
0.3200, -7.0000, 7.0000, 1.2900
testing/wikipedia/v3/00254.html
d
d
x
log
b
(
x
)
=
1
x
ln
(
b
)
.
Doc 30
0.2542, -10.0000, 6.0000, 0.2542
testing/wikipedia/v3/00580.html
d
y
d
x
|
x
=
a
=
d
y
d
x
(
a
)
.
Doc 12
0.3200, -7.0000, 7.0000, 1.2900
testing/wikipedia/v3/00254.html
ψ
i
m
(
0
)
=
0
,
d
ψ
i
m
d
x
(
0
)
=
1.
Doc 31
0.2542, -13.0000, 6.0000, 0.2542
testing/wikipedia/v3/10973.html
d
y
d
x
|
x
=
a
=
d
y
d
x
(
a
)
.
Doc 32
0.2542, -13.0000, 5.0000, 0.2542
testing/wikipedia/v3/16694.html
d
d
x
(
1
2
(
d
t
d
x
)
-
2
)
=
f
(
x
)
Doc 33
0.2542, -14.0000, 6.0000, 0.2542
testing/wikipedia/v3/03906.html
d
d
x
arcsin
(
x
)
=
1
1
-
x
2
,
-
1
<
x
<
1.
Doc 12
0.3200, -7.0000, 7.0000, 1.2900
testing/wikipedia/v3/00254.html
d
2
u
d
y
2
=
1
μ
d
p
d
x
,
Doc 34
0.2383, -10.0000, 5.0000, 0.2383
testing/wikipedia/v3/09871.html
d
I
d
t
(
0
)
>
0
,
Doc 35
0.2243, -4.0000, 5.0000, 0.2243
testing/wikipedia/v3/07098.html
=
d
d
t
(
y
˙
x
˙
)
1
x
˙
Doc 36
0.2243, -9.0000, 4.0000, 0.6070
testing/wikipedia/v3/09417.html
D
=
d
d
x
,
Doc 37
0.2073, -2.0000, 3.0000, 0.2073
testing/wikipedia/v3/03183.html
θ
(
x
)
=
d
w
d
x
Doc 38
0.2073, -4.0000, 3.0000, 0.3673
testing/wikipedia/v3/09923.html
p
=
d
f
d
x
(
x
)
,
Doc 39
0.2073, -5.0000, 5.0000, 0.2073
testing/wikipedia/v3/04480.html
d
S
d
E
=
1
T
,
Doc 40
0.2073, -5.0000, 4.0000, 0.2073
testing/wikipedia/v3/09920.html
d
s
d
φ
=
1
κ
,
Doc 41
0.2073, -5.0000, 4.0000, 0.2073
testing/wikipedia/v3/22518.html
f
′
(
x
)
=
d
y
d
x
Doc 42
0.2073, -5.0000, 3.0000, 0.2073
testing/wikipedia/v3/09549.html
1
T
=
d
S
d
E
,
Doc 43
0.2073, -5.0000, 3.0000, 0.2073
testing/wikipedia/v3/01344.html
d
d
x
ln
x
=
1
x
,
Doc 17
0.3011, -7.0000, 6.0000, 0.5083
testing/wikipedia/v3/00594.html
=
d
d
x
(
d
y
d
x
)
Doc 36
0.2243, -9.0000, 4.0000, 0.6070
testing/wikipedia/v3/09417.html
ψ
(
x
)
=
d
ρ
(
x
)
d
x
Doc 44
0.2073, -6.0000, 3.0000, 0.2073
testing/wikipedia/v3/11261.html
d
d
x
ln
(
x
)
=
1
x
.
Doc 3
0.4412, -3.0000, 9.0000, 0.6484
testing/wikipedia/v3/00699.html
f
′
(
x
)
=
d
d
x
f
(
x
)
Doc 45
0.2073, -7.0000, 3.0000, 0.2073
testing/wikipedia/v3/12599.html
f
(
x
)
=
d
F
(
x
)
d
x
.
Doc 46
0.2073, -7.0000, 3.0000, 0.2073
testing/wikipedia/v3/00771.html
f
(
x
)
=
1
2
(
a
x
+
x
)
Doc 47
0.2073, -8.0000, 4.0000, 0.2073
testing/wikipedia/v3/15214.html
f
(
x
)
=
1
2
(
x
+
2
x
)
Doc 48
0.2073, -8.0000, 4.0000, 0.2073
testing/wikipedia/v3/15245.html
d
d
x
arctan
(
x
)
=
1
1
+
x
2
Doc 12
0.3200, -7.0000, 7.0000, 1.2900
testing/wikipedia/v3/00254.html
d
x
d
t
=
k
b
[
A
]
0
x
e
(
x
e
-
x
)
Doc 49
0.2073, -14.0000, 2.0000, 0.2073
testing/wikipedia/v3/09082.html
P
n
(
x
)
=
d
n
d
x
n
(
x
n
(
1
-
x
)
n
)
.
Doc 50
0.2073, -15.0000, 5.0000, 0.2073
testing/wikipedia/v3/17238.html
H
=
1
2
(
x
p
+
p
x
)
=
-
i
(
x
d
d
x
+
1
2
)
.
Doc 51
0.2073, -20.0000, 3.0000, 0.2073
testing/wikipedia/v3/05993.html
d
y
d
x
=
1
x
d
ϕ
d
t
Doc 52
0.1875, -8.0000, 5.0000, 0.1875
testing/wikipedia/v3/07349.html
f
m
=
1
ρ
d
p
d
x
.
Doc 53
0.1754, -8.0000, 2.0000, 0.1754
testing/wikipedia/v3/03849.html
d
y
d
x
=
1
5
y
4
-
1
,
Doc 28
0.2542, -7.0000, 6.0000, 0.4297
testing/wikipedia/v3/03420.html
d
y
d
x
=
y
˙
x
˙
=
3
8
t
,
Doc 36
0.2243, -9.0000, 4.0000, 0.6070
testing/wikipedia/v3/09417.html
D
=
d
d
x
Doc 54
0.1600, -2.0000, 4.0000, 0.1600
testing/wikipedia/v3/06039.html
Doc 55
0.1600, -2.0000, 4.0000, 0.1600
testing/wikipedia/v3/30289.html
d
y
d
x
,
Doc 8
0.3478, -10.0000, 6.0000, 0.5078
testing/wikipedia/v3/01064.html
=
d
x
d
t
Doc 56
0.1600, -2.0000, 3.0000, 0.1600
testing/wikipedia/v3/21943.html
d
y
d
x
=
s
a
,
Doc 57
0.1600, -6.0000, 4.0000, 0.1600
testing/wikipedia/v3/00225.html
d
y
d
x
=
1
2
y
Doc 58
0.1600, -6.0000, 4.0000, 0.1600
testing/wikipedia/v3/15372.html
d
x
d
y
=
1
y
2
Doc 59
0.1600, -6.0000, 3.0000, 0.1600
testing/wikipedia/v3/12494.html
1
ρ
=
d
2
w
d
x
2
Doc 38
0.2073, -4.0000, 3.0000, 0.3673
testing/wikipedia/v3/09923.html
1
Λ
(
𝐧
)
=
d
X
d
x
Doc 60
0.1600, -7.0000, 4.0000, 0.3200
testing/wikipedia/v3/10201.html
d
d
x
ln
x
=
1
x
.
Doc 61
0.1600, -7.0000, 4.0000, 0.1600
testing/wikipedia/v3/12783.html
κ
=
1
r
d
p
d
r
,
Doc 62
0.1600, -7.0000, 3.0000, 0.1600
testing/wikipedia/v3/25927.html
d
y
d
x
=
1
1
+
x
2
Doc 25
0.2542, -6.0000, 6.0000, 0.8285
testing/wikipedia/v3/17871.html
d
d
x
log
e
x
=
1
x
.
Doc 65
0.1600, -8.0000, 4.0000, 0.1600
testing/wikipedia/v3/00335.html
d
d
x
hacovercosin
(
x
)
=
cos
x
2
Doc 63
0.1600, -8.0000, 4.0000, 0.6400
testing/wikipedia/v3/05549.html
d
d
x
haversin
(
x
)
=
sin
x
2
Doc 63
0.1600, -8.0000, 4.0000, 0.6400
testing/wikipedia/v3/05549.html
y
cot
φ
=
y
d
y
d
x
,
Doc 64
0.1600, -8.0000, 4.0000, 0.1600
testing/wikipedia/v3/05052.html
d
d
x
log
(
κ
)
=
κ
′
κ
Doc 66
0.1600, -8.0000, 4.0000, 0.1600
testing/wikipedia/v3/15335.html
1
Λ
(
𝐧
)
=
d
X
d
x
.
Doc 60
0.1600, -7.0000, 4.0000, 0.3200
testing/wikipedia/v3/10201.html
T
=
1
2
(
d
s
d
t
)
2
Doc 67
0.1600, -8.0000, 3.0000, 0.1600
testing/wikipedia/v3/12841.html
d
d
x
hacoversin
(
x
)
=
-
cos
x
2
Doc 63
0.1600, -8.0000, 4.0000, 0.6400
testing/wikipedia/v3/05549.html
d
d
x
havercosin
(
x
)
=
-
sin
x
2
Doc 63
0.1600, -8.0000, 4.0000, 0.6400
testing/wikipedia/v3/05549.html
d
y
d
x
=
1
1
-
x
2
Doc 25
0.2542, -6.0000, 6.0000, 0.8285
testing/wikipedia/v3/17871.html
d
d
x
arcoth
x
=
1
1
-
x
2
Doc 68
0.1600, -9.0000, 4.0000, 0.3200
testing/wikipedia/v3/01762.html
d
d
x
artanh
x
=
1
1
-
x
2
Doc 68
0.1600, -9.0000, 4.0000, 0.3200
testing/wikipedia/v3/01762.html
d
x
d
t
=
1
H
ν
(
x
)
,
Doc 69
0.1600, -9.0000, 3.0000, 0.1600
testing/wikipedia/v3/22001.html
a
=
1
2
(
d
d
q
+
q
)
Doc 70
0.1600, -9.0000, 3.0000, 0.1600
testing/wikipedia/v3/06286.html
d
d
x
χ
2
(
x
)
=
arctanh
x
x
.
Doc 71
0.1600, -10.0000, 4.0000, 0.1600
testing/wikipedia/v3/08077.html
f
5
(
x
)
=
log
c
x
,
c
≠
0
,
1
Doc 72
0.1600, -10.0000, 3.0000, 0.1600
testing/wikipedia/v3/03755.html
E
=
1
2
(
d
x
d
z
)
2
+
Φ
(
x
)
Doc 73
0.1600, -12.0000, 3.0000, 0.1600
testing/wikipedia/v3/16445.html
G
1
(
i
)
=
1
z
i
d
G
0
(
i
)
d
x
|
x
=
1
Doc 74
0.1600, -15.0000, 4.0000, 0.1600
testing/wikipedia/v3/15814.html
D
q
=
1
x
q
d
d
(
ln
x
)
-
1
q
-
1
,
Doc 75
0.1600, -16.0000, 4.0000, 0.1600
testing/wikipedia/v3/12695.html
j
n
(
x
)
=
(
-
x
)
n
(
1
x
d
d
x
)
n
sin
(
x
)
x
,
Doc 76
0.1600, -20.0000, 4.0000, 0.1600
testing/wikipedia/v3/00134.html