DERIVATIVES AND INTEGRALS

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DERIVATIVES AND INTEGRALS
DERIVATIVES AND INTEGRALS
Basic Differentiation Rules
1.
4.
7.
10.
13.
16.
19.
22.
25.
28.
31.
34.
d
cu cu
dx
d u
vu uv
dx v
v2
d
x 1
dx
d u
e eu u
dx
d
sin u cos uu
dx
d
cot u csc2 uu
dx
d
u
arcsin u dx
1 u2
d
u
arccot u dx
1 u2
d
sinh u cosh uu
dx
d
coth u csch2 uu
dx
d
u
sinh1 u dx
u2 1
d
u
coth1 u dx
1 u2
2.
5.
8.
11.
14.
17.
20.
23.
26.
29.
32.
35.
d
u ± v u ± v
dx
d
c 0
dx
d
u
u
u , u 0
dx
u
d
u
loga u dx
ln au
d
cos u sin uu
dx
d
sec u sec u tan uu
dx
d
u
arccos u dx
1 u2
d
u
arcsec u dx
u u2 1
d
cosh u sinh uu
dx
d
sech u sech u tanh uu
dx
d
u
cosh1 u dx
u2 1
d
u
sech1 u dx
u1 u2
3.
5.
7.
9.
11.
13.
15.
17.
kf u du k f u du
2.
du u C
4.
eu du eu C
6.
cos u du sin u C
8.
cot u du ln sin u C
10.
csc u du ln csc u cot u C
12.
csc2 u du cot u C
14.
csc u cot u du csc u C
16.
du
1
u
arctan C
2
u
a
a
18.
a2
© Houghton Mifflin Company, Inc.
6.
9.
Basic Integration Formulas
1.
3.
12.
15.
18.
21.
24.
27.
30.
33.
36.
d
uv uv vu
dx
d n
u nu n1u
dx
d
u
ln u dx
u
d u
a ln aau u
dx
d
tan u sec2 uu
dx
d
csc u csc u cot uu
dx
d
u
arctan u dx
1 u2
d
u
arccsc u dx
u u2 1
d
tanh u sech2 uu
dx
d
csch u csch u coth uu
dx
d
u
tanh1 u dx
1 u2
u
d
csch1 u dx
u 1 u2
f u ± gu du au du ln1aa
u
f u du ±
C
sin u du cos u C
tan u du ln cos u C
sec u du ln sec u tan u C
sec2 u du tan u C
sec u tan u du sec u C
du
u
C
a
du
1
u
arcsec
C
2
2
a
a
uu a
a2 u2
arcsin
gu du

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