Derivatives And Integrals

Question 0

Quotient rule of derivatives

Answer 0

(vu’-uv’)/v^2

Question 1

Product rule

Answer 1

uv’+vu’

Question 2

Derivative of u^n (exponent rule of derivatives)

Answer 2

nu^(n-1)u’

Question 3

Derivative of |u|

Answer 3

uu’/|u|

Question 4

Derivative of e^u

Answer 4

e^u u’

Question 9

Derivative of cot(u)

Answer 9

-csc^2(u)u’

Question 10

Derivative of ln u

Answer 10

u’/u

Question 11

Derivative of csc(u)

Answer 11

-csc(u)cot(u)u’

Question 12

Derivative of sin(u)

Answer 12

Cos(u)u’

Question 13

Derivative of arccos(u)

Answer 13

-u’/sqrt(1-u^2)

Question 14

Derivative of cos(u)

Answer 14

-sin(u)u’

Question 15

Derivative of arccot(u)

Answer 15

-u’/(1+u^2)

Question 17

Derivative of arccsc(u)

Answer 17

-u’/|u|*sqrt(u^2-1)

Question 18

Integral of (1/u)du

Answer 18

Ln|u|+C

Question 19

Exponent rule for integrals(integral of u^n)

Answer 19

u^(n+1)/(n+1)+C

Question 20

Integral of sin(u)

Answer 20

-cos(u)+C

Question 21

Integral of cos(u)

Answer 21

sin(u)+C

Question 22

Integral of tan(u)

Answer 22

-ln|cos(u)|+C

Question 23

Integral of cot(u)

Answer 23

ln|sin(u)|+C

Question 24

Integral of sec(u)

Answer 24

ln|sec(u)+tan(u)|

Question 25

Integral of csc(u)

Answer 25

-ln|csc(u)+cot(u)|+C

Question 26

Integral of sec^2(u)

Answer 26

tan(u)+C

Question 27

Integral of cot^2(u)

Answer 27

-cot(u)+C

Question 28

Integral of sec(u)tan(u)

Answer 28

sec(u)+C

Question 29

Integral of csc(u)cot(u)

Answer 29

-csc(u)+C

Question 30

Derivative of tan(u)

Answer 30

Sec^2(u)u’

Question 33

Derivative of arcsin(u)

Answer 33

u’/sqrt(1-u^2)

Question 35

Derivative of arctan(u)

Answer 35

u’/1+u^2

Question 36

Derivative of sec(u)

Answer 36

Sec(u)tan(u)u’

Question 37

Derivative of arcsec(u)

Answer 37

u’/u*sqrt(u^2-1)