Lucas

Question 1

d/dx * (sinx) =

Answer 1

cos(x)

Question 2

d/dx * (cosx) =

Answer 2

-sin(x)

Question 3

d/dx * (tanx) =

Answer 3

sec^2 (x)

Question 4

d/dx * (cscx) =

Answer 4

-cscxcotx

Question 5

d/dx * (secx) =

Answer 5

secxtanx

Question 6

d/dx * (cotx) =

Answer 6

• csc^2(x)

Question 7

sin^2(x) + cos^2(x) =

Answer 7

1

Question 8

1 - cos^2(x) =

Answer 8

sin^2(x)

Question 9

1 - sin^2(x) =

Answer 9

cos^2(x)

Question 10

tan^2(x) + 1 =

Answer 10

sec^2(x)

Question 11

sec^2(x) - 1 =

Answer 11

tan^2(x)

Question 12

cot^2(x) + 1 =

Answer 12

csc^2(x)

Question 13

csc^2(x) - 1 =

Answer 13

cot^2(x)

Question 14

∫sec(x)dx

Answer 14

ln| secx + tanx | + C

Question 15

sin(2x) =

Answer 15

2sinxcosx

Question 16

∫sin(x)dx =

Answer 16

• cosx + C

Question 17

∫sec^2(x) =

Answer 17

tanx + C

Question 18

∫1/(x^2 + 1)dx =

Answer 18

arctan(x)

Question 19

∫dx/x =

Answer 19

ln |x| + C

Question 20

∫b^x dx =

Answer 20

(b^x) / ln(b) + C

Question 21

∫cos(x)dx =

Answer 21

sin(x) +C

Question 22

∫csc^2 (x) =

Answer 22

-cot(x) + C

Question 23

∫1/(1 - x^2)^(1/2) =

Answer 23

arcsin(x) +C

Question 24

∫sec(x)tan(x)dx =

Answer 24

sec(x) + C

Question 25

∫csc(x)dx =

Answer 25

ln|cscx - cotx| + C

Question 26

tan(2x) =

Answer 26

2tan(x) / (1 - tan^2(x))

Question 27

cos(2x) =

Answer 27

cos^2(x) - sin^2(x)

2cos^2(x) - 1

1 - sin^2(x)

Question 28

∫arcsin(x)dx =

Answer 28

(x)arcsin(x) + (1 + x^2)^(1/2) + C

Question 29

∫arccos(x)dx =

Answer 29

(x)arccos(x) - (1 - x^2)^(1/2) + C

Question 30

∫arctan(x)dx =

Answer 30

(x)arctan(x) - (1 / 2) * ln( 1 + x^2) + C

Question 31

∫arccsc(x)dx =

Answer 31

(x)arccsc(x) + ln(x + (x^2 - 1)^(1/2 ))+ C

Question 32

∫arcsec(x)dx =

Answer 32

(x)arcsec(x) - ln(x + (x + (x^2 +1)^(1/2)) + C

Question 33

∫arccot(x)dx =

Answer 33

(x)arccot(x) + (1 / 2) * ln(1 + x^2) +C

Question 34

d/dx arcsin(x) =

Answer 34

1 / ((1-x^2)^(1/2))

Question 35

d/dx arccos(x) =

Answer 35

• 1 / ((1- x^2)^(1/2))

Question 36

d/dx arctan(x) =

Answer 36

1 / (1 + x^2)

Question 37

d/dx arccot(x) =

Answer 37

-1 / (1+ x^2)

Question 38

d/dx arcsec(x) =

Answer 38

1 / (|x| * (x^2 - 1)^(1/2))

Question 39

d/dx arccsc(x) =

Answer 39

-1 / (|x| * (x^2 - 1)^(1/2))