derivatives and integrals

Question 1

d/dx [cx]

Answer 1

cx’

Question 2

d/dx [xy]

Answer 2

xy’ + yx’

Question 3

d/dx [c]

Answer 3

0

Question 4

d/dx [x]

Answer 4

1

Question 5

d/dx [lnx]

Answer 5

1/x (x’)

Question 6

d/dx [loga x]

Answer 6

1/ln(a) (1/x) (x’)

Question 7

d/dx [sin x]

Answer 7

cos x (x’)

Question 8

d/dx [tan x]

Answer 8

sec²x (x’)

Question 9

d/dx [sec x]

Answer 9

secxtanx (x’)

Question 10

d/dx [arcsinx]

Answer 10

x’/(√1-x²)

Question 11

d/dx [arctanx]

Answer 11

x’/(1+x²)

Question 12

d/dx [arcsec]

Answer 12

x’/(|x|√x²-1)

Question 13

d/dx [x +/- y]

Answer 13

x’ +/- y’

Question 14

d/dx [x/y]

Answer 14

(yx’ - xy’)/y²

Question 15

d/dx [x^n]

Answer 15

nx^n-1x’

Question 16

d/dx [|x|]

Answer 16

x/|x| (x’) ; x CANNOT = 0

Question 17

d/dx [e^x]

Answer 17

e^x(x’)

Question 18

d/dx [a^x]

Answer 18

(ln a)(a^x)(x’)

Question 19

d/dx [cosu]

Answer 19

-sinx (x’)

Question 20

d/dx [cotx]

Answer 20

-csc²x (x’)

Question 21

d/dx [cscx]

Answer 21

-cscxcotx (x’)

Question 22

d/dx [arccosx]

Answer 22

-x’/(√1-x²)

Question 23

d/dx [arccotx]

Answer 23

-x’/(1+x²)

Question 24

d/dx [arccscx]

Answer 24

-x’/(|x|√x²-1)

Question 25

∫ k f(x) dx

Answer 25

k ∫ f(x) dx

Question 26

∫ dx

Answer 26

x + C

Question 27

∫ 1/x dx

Answer 27

ln |x| + C

Question 28

∫ a^x dx

Answer 28

(1/lna) (a^x) + C

Question 29

∫ cosx dx

Answer 29

sinx + C

Question 30

∫ cotx dx

Answer 30

ln|sinx| + C

Question 31

∫ cscx dx

Answer 31

-ln|cscx + cotx| + C

Question 32

∫ csc²x dx

Answer 32

-cotx + C

Question 33

∫ cscxcotx dx

Answer 33

-cscx + C

Question 34

∫ 1/(a²+x²) dx

Answer 34

1/a arctan x/a + C

Question 35

∫ [f(x) +/- g(x)] dx

Answer 35

∫ f(x) dx +/- ∫ g(x) dx

Question 36

∫ x^n dx

Answer 36

(x^n+1)/(n+1)

Question 37

∫ e^x dx

Answer 37

e^x + C

Question 38

∫ sinx dx

Answer 38

-cosx + C

Question 39

∫ tanx dx

Answer 39

-ln|cosx| +C

Question 40

∫ secx dx

Answer 40

ln|secx + tanx| + C

Question 41

∫ sec²x dx

Answer 41

tanx + C

Question 42

∫ secxtanx dx

Answer 42

secx + C

Question 43

∫ 1/(√a²-x²) dx

Answer 43

arcsin x/a + C

Question 44

∫ 1/(x√x²-a²) dx

Answer 44

(1/a) arcsec|x|/a +C