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Integration and Differentiation Cheat Sheet, Cheat Sheet of Calculus

University of California - DavisCalculus

Basic Differentiation Rules , Basic Integration Formulas

Typology: Cheat Sheet

2020/2021

Uploaded on 04/27/2021

ekobar
ekobar 🇺🇸

4.3

(32)

261 documents

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Basic Differentiation Rules
Basic Integration Formulas
DERIVATIVES AND INTEGRALS
1.
4.
7.
10.
13.
16.
19.
22.
25.
28.
31.
34.
2.
5.
8.
11.
14.
17.
20.
23.
26.
29.
32.
35.
3.
6.
9.
12.
15.
18.
21.
24.
27.
30.
33.
36. d
dx
csch
1
u
u
u
1u
2
d
dx
tanh
1
u
u
1u
2
d
dx
csch u

csch u coth u
u
d
dx
tanh u
sech
2
u
u
d
dx
arccsc u
u
u
u
2
1
d
dx
arctan u
u
1u
2
d
dx
csc u

csc u cot u
u
d
dx
tan u
sec
2
u
u
d
dx
a
u
ln a
a
u
u
d
dx
ln u
u
u
d
dx
u
n
nu
n1
u
d
dx
uv
uv
vu
d
dx
sech
1
u
u
u
1u
2
d
dx
cosh
1
u
u
u
2
1
d
dx
sech u

sech u tanh u
u
d
dx
cosh u
sinh u
u
d
dx
arcsec u
u
u
u
2
1
d
dx
arccos u
u
1u
2
d
dx
sec u
sec u tan u
u
d
dx
cos u

sin u
u
d
dx
log
a
u
u
ln a
u
u0
d
dx
u
u
u
u
,
d
dx
c
0
d
dx
u
±
v
u
±
v
d
dx
coth
1
u
u
1u
2
d
dx
sinh
1
u
u
u
2
1
d
dx
coth u

csch
2
u
u
d
dx
sinh u
cosh u
u
d
dx
arccot u
u
1u
2
d
dx
arcsin u
u
1u
2
d
dx
cot u

csc
2
u
u
d
dx
sin u
cos u
u
d
dx
e
u
e
u
u
d
dx
x
1
d
dx
u
v
vu
uv
v
2
d
dx
cu
cu
1.
3.
5.
7.
9.
11.
13.
15.
17.
2.
4.
6.
8.
10.
12.
14.
16.
18. du
u
u
2
a
2
1
a arcsec
u
aC
du
a
2
u
2
arcsin u
aC
sec u tan u du sec uC
sec
2
u du tan uC
sec u du ln
sec utan u
C
tan u du ln
cos u
C
sin u du cos uC
a
u
du
1
ln a
a
u
C
f
u
±
g
u

du f
u
du
±
g
u
du
du
a
2
u
2
1
a arctan u
aC
csc u cot u
du csc uC
csc
2
u du cot uC
csc u du ln
csc ucot u
C
cot u du ln
sin u
C
cos u du sin uC
e
u
du e
u
C
du uC
kf
u
du kf
u
du

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Basic Differentiation Rules

Basic Integration Formulas

DERIVATIVES AND INTEGRALS

36. dxd csch^1 u  u 1 u ^  u 2

dx^ d tanh^1 u^ ^1 u^  u^2

dx^ d csch^ u^  csch^ u^ coth^ uu

dx^ d tanh^ u^ ^ sech^2 uu

dx^ d arccsc^ u^ ^ u^ 

uu^2 ^1

dx^ d arctan^ u^ ^1 u^  u^2

dx^ d csc^ u^  csc^ u^ cot^ uu^ 

dx^ d tan^ u^ ^ sec^2 uu^ 

dx^ d au^ ^ ln^ aau^ u

dx^ d ln^ u^ ^ u u^ 

dxd u^ n^ ^ nu^ n^1 u^ 

dx^ d uv^ ^ uv^ ^ ^ vu^ 

dx^ d sech^1 u^ ^ u^ 

u 1  u^2

dx^ d cosh^1 u^ ^ u

u^2  1

dx^ d sech^ u^  sech^ u^ tanh^ uu

dx^ d cosh^ u^ ^ sinh^ uu

dx^ d arcsec^ u^ ^ u^ 

uu^2 ^1

dx^ d arccos^ u^ ^ u^ 

 1  u^2

dx^ d sec^ u^ ^ sec^ u^ tan^ uu^ 

dx^ d cos^ u^  sin^ uu^ 

d

dx loga^ u^ ^

u

ln au

dx^ d u^ ^ uu u^ , u^ ^0

dx^ d c^ ^0

dx^ d u^ ±^ v^ ^ u^ ^ ±^ v^ 

dx^ d coth^1 u^ ^1 u^  u^2

dx^ d sinh^1 u^ ^ u^ 

u^2  1

dx^ d coth^ u^  csch^2 uu

dx^ d sinh^ u^ ^ cosh^ uu

dx^ d arccot^ u^ ^1 u u^2

dx^ d arcsin^ u^ ^ u^ 

 1  u^2

dx^ d cot^ u^  csc^2 uu^ 

dx^ d sin^ u^ ^ cos^ uu^ 

dx^ d eu^ ^ eu^ u^ 

dx^ d x^ ^1

dx^ d uv^ ^ vu^ ^  v^2 uv^ 

dx^ d cu^ ^ cu^ 

18. uudu 2  a 2  1 a arcsec u a  C

^ du a^2  u^2 ^ arcsin^

ua  C

sec u tan u du  sec u  C

sec^2 u du  tan u  C

sec u du  lnsec u  tan u  C

tan u du  lncos u  C

sin u du  cos u  C

au^ du  (^) ln^1 a au^  C

 fu ± gu du  f u du ± gu du

a^2 du u^2 ^1 a arctan^ ua ^ C

csc u cot u du  csc u  C

csc^2 u du  cot u  C

csc u du  lncsc u  cot u  C

cot u du  lnsin u  C

cos u du  sin u  C

eu^ du  eu^  C

du  u  C

kfu du  k fu du