Maths
Calculus - Differentiation
General Differentials
d
d
x
k
=
0
d
d
x
x
=
1
d
d
x
uv
=
u
d
v
d
x
+
v
d
u
d
x
d
d
x
u
v
=
(
v
d
u
d
x
−
u
d
v
d
x
)
v
2
d
y
d
x
=
d
y
d
t
⋅
d
t
d
x
d
d
x
x
n
=
nx
n
−
1
ⅆ
ⅆ
x
log
a
x
=
1
x
log
a
e
,
a
>
0
,
a
&neq;
1
d
d
x
e
x
=
e
x
d
d
x
a
x
(
for
a
>
0
)
=
a
x
(
ln
a
)
d
d
x
ln
x
(
for
x
>
0
)
=
1
x
Trigonometric Differentials
d
d
x
sin
x
=
cos
x
d
d
x
cos
x
=
-
sin
x
d
d
x
tan
x
=
sec
2
x
d
d
x
csc
x
=
-
csc
x
cot
x
d
d
x
sec
x
=
sec
x
tan
x
d
d
x
cot
x
=
-
csc
2
x
d
d
x
sinh
x
=
cosh
x
d
d
x
cosh
x
=
sinh
x
d
d
x
tan
-
1
x
=
1
1
+
x
2
d
d
x
sin
-
1
x
=
1
1
-
x
2
d
d
x
cos
-
1
x
=
-
1
1
-
x
2
d
d
x
cot
-
1
x
=
-
1
1
+
x
2
d
d
x
sec
-
1
x
=
1
x
x
2
-
1
d
d
x
csc
-
1
x
=
-
1
x
x
2
-
1
d
d
x
sinh
-
1
(
x
a
)
=
1
a
2
+
x
2
d
d
x
cosh
-
1
(
x
a
)
=
1
x
2
-
a
2
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