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Differentiation Formulas
This page contains a list of commonly used differentiation formulas.
x
1.
Derivative of a Constant (k):
[]
0
d
k
dx
=
2.
ConstantMultiple Rule:
()
'
d
kfx
kf x
dx
⋅=
⋅
3.
Sum/Difference Rule:
[()
]
'
'
d
f
xg
x
f
x
dx
±=±
4.
Power Rule:
1
rr
d
x
rx
dx
−
⎡⎤
=
⎣⎦
5.
Product Rule:
[ ()()
]
() '
'
d
f xgx
f xg x
gx f x
dx
=+
6.
Quotient Rule:
2
'
() ()
'
df
x
fx
g
x
f
x
dx
g x
gx
−
=
⎢⎥
7.
Reciprocal Rule:
2
1'
]
dg
dx
g x
g x
−
=
(
)
x
8.
Chain Rule:
()
' ()
'
d
f gx
f gx g x
dx
=
9.
x
d
ee
dx
=
10.
1
ln( )
(
0)
d
xx
dx
x
=
>
11.
ln
d
aaa
dx
=⋅
12.
1
log
ln
a
d
x
dx
x
a
=
13.
sin
cos
d
x
x
dx
=
14.
cos
sin
d
x
x
dx
=−
15.
2
tan
sec
d
x
x
dx
=
16.
sec
sec
tan
d
x
dx
=
17.
csc
csc
cot
d
x
dx
18.
2
cot
csc
d
x
x
dx
19.
1
2
1
sin
1
d
x
dx
−
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This note was uploaded on 06/17/2008 for the course M 408 L taught by Professor Cepparo during the Spring '08 term at University of Texas.
 Spring '08
 Cepparo
 Power Rule, Product Rule, Quotient Rule, Formulas

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