Formula Test

Question 1

d/dx [cu]

Answer 1

cu’

Question 2

d/dx [uv]

Answer 2

uv’ + vu’

Question 3

d/dx [u+-v]

Answer 3

u’+-v’

Question 4

d/dx [u/v]

Answer 4

(vu’-uv’)/v^2

Question 5

d/dx [c]

Answer 5

0

Question 6

d/dx [u^n]

Answer 6

nu^(n-1)u’

Question 7

d/dx [x]

Answer 7

1

Question 8

d/dx [|u|]

Answer 8

(u/|u|)u’

Question 9

d/dx [lnu]

Answer 9

u’/u

Question 10

d/dx [e^u}

Answer 10

u’e^u

Question 11

d/dx [sinu]

Answer 11

(cosu)u’

Question 12

d/dx [cosu]

Answer 12

-(sinu)u’

Question 13

d/dx [tanu]

Answer 13

(sec^2u)u’

Question 14

d/dx [cotu]

Answer 14

-(csc^2u)u’

Question 15

d/dx [secu]

Answer 15

(secutanu)u’

Question 16

d/dx [cscu]

Answer 16

-(cscucotu)u’

Question 17

d/dx [arcsinu]

Answer 17

u’/(sqrrt(1-u^2))

Question 18

d/dx [arccos]

Answer 18

-u’/(sqrrt(1-u^2))

Question 19

d/dx [arctanu]

Answer 19

u’/(1+u^2)

Question 20

d/dx [arccotu]

Answer 20

-u’/(1+u^2)

Question 21

d/dx [arcsecu]

Answer 21

u’/(|u|sqrrt(u^2-1))

Question 22

d/dx [arccscu)

Answer 22

-u’/(|u|sqrrt(u^2-1))

Question 23

∫ kf(u) du

Answer 23

k∫ f(u) du

Question 24

∫ [f(u) +- g(u)] du

Answer 24

∫ f(u) du +- ∫ g(u) du

Question 25

∫ du

Answer 25

u + C

Question 26

∫ u^n

Answer 26

u^n+1 / n+1 + C

Question 27

∫ du/u

Answer 27

ln|u| + C

Question 28

∫ e^u du

Answer 28

e^u + C

Question 29

∫ sinu du

Answer 29

-cosu + C

Question 30

∫ cosu du

Answer 30

sinu + C

Question 31

∫ tanu du

Answer 31

-ln|cosu| +C

Question 32

∫ cotu du

Answer 32

ln|sinu| + C

Question 33

∫ secu du

Answer 33

ln|secu + tanu| + C

Question 34

∫ cscu du

Answer 34

-ln|cscu + cotu| + C

Question 35

∫ sec^2u du

Answer 35

tanu + C

Question 36

∫ csc^2u du

Answer 36

-cotu + C

Question 37

∫ secutanu du

Answer 37

secu +C

Question 38

∫ cscucotu du

Answer 38

-cscu + C