Differentiation and Integration Rules

Question 1

d/dx of cu

Answer 1

cu’

Question 2

d/dx u +/- v

Answer 2

u’ +/- v’

Question 3

d/dx uv

Answer 3

uv’ + vu’

Question 4

d/dx u/v

Answer 4

vu’-uv’ all over v^2

Question 5

d/dx c

Answer 5

0

Question 6

d/dx u^n

Answer 6

n * u^n-1 * u’

Question 7

d/dx x

Answer 7

1

Question 8

d/dx |u|

Answer 8

u/|u| * u’ (u not equal to 0)

Question 9

d/dx Ln u

Answer 9

1/u * u’

Question 10

d/dx e^u

Answer 10

e^u * u’

Question 11

d/dx logaU

Answer 11

1/Ln a * 1/u *u’

Question 12

d/dx a^u

Answer 12

Ln a * a^u * u’

Question 13

d/dx sin u

Answer 13

Cos u * u’

Question 14

d/dx cos u

Answer 14

-sin u *u’

Question 15

d/dx tan u

Answer 15

Sec^2 u *u’

Question 16

d/dx Cot u

Answer 16

-Csc^2 u * u’

Question 17

d/dx sec u

Answer 17

Sec u * tan u * u’

Question 18

d/dx Csc u

Answer 18

-Csc u * cot u * u’

Question 19

d/dx arcsin u

Answer 19

1/Square root of 1-u^2

Times u’

Question 20

d/dx arccos u

Answer 20

-1/Square root of 1-u^2

Times u’

Question 21

d/dx arctan u

Answer 21

1/1+u^2 * u’

Question 22

d/dx arccot u

Answer 22

-1/1+u^2 * u’

Question 23

d/dx arcsec u

Answer 23

1/absolute value of u * 1/Square root of u^2-1 *u’

Question 24

d/dx arccsc u

Answer 24

-1/absolute value of u * 1/Square root of u^2-1 *u’

Question 25

{k*f(u)

Answer 25

K{f(u)

Question 26

{f(u)+/-g(u)

Answer 26

{f(u) +/- {g(u)

Question 27

{du

Answer 27

U + C

Question 28

{u^n

Answer 28

1/n+1 * u^n+1 + C (n not equal to -1)

Question 29

{du/u

Answer 29

Ln |u| + C

Question 30

{e^u du

Answer 30

E^u + C

Question 31

{a^u de

Answer 31

1/Ln a * a^u + C

Question 32

{sin u du

Answer 32

-cos u + C

Question 33

{cos u du

Answer 33

Sin u + C

Question 34

{tan u du

Answer 34

-ln|cos u| + C

Question 35

{cot u du

Answer 35

Ln|sin u| + C

Question 36

{sec u du

Answer 36

Ln|sec u + tan u| + C

Question 37

{csc u du

Answer 37

-ln|csc u + cot u| +C

Question 38

{du/Square root of a^2-u^2

Answer 38

Arc sin u/a + C

Question 39

{du/a^2+u^2

Answer 39

1/a arctan u/a + C

Question 40

{du/u*Square root of u^2-a^2

Answer 40

1/a arcsec |u|/a + C

Question 41

{Sec^2 u du

Answer 41

Tan u + C

Question 42

{Csc^2 u du

Answer 42

-Cot u +C

Question 43

{Sec u * tan u du

Answer 43

Sec u + C

Question 44

{Csc u * cot u du

Answer 44

-Csc u + C

Question 45

{Y'=ky

Answer 45

Y=Ce^kx

Question 46

{Y'=ky(1-y/L)

Answer 46

Y=L/(1+be^-kt)

Question 47

The integration of udv

Answer 47

U*V minus the integration of vdu