Derivatives, Integrals, Identities, Formulas

Question 1

Derivative of sin(x)

Answer 1

cos(x)

Question 2

Derivative of cos(x)

Answer 2

-sin(x)

Question 3

Derivative of cot(x)

Answer 3

-csc²(x)

Question 4

Derivative of tan(x)

Answer 4

sec²(x)

Question 5

Derivative of sec(x)

Answer 5

sec(x)tan(x)

Question 6

Derivative of csc(x)

Answer 6

-csc(x)cot(x)

Question 7

csc(x) to what?

Pythagorean Identity

Answer 7

1/sin(x)

Question 8

cos(x) to what?

Pythagorean Identity

Answer 8

1/sec(x)

Question 9

sec(x) to what?

Pythagorean Identity

Answer 9

1/cos(x)

Question 10

cot(x) to what?

Pythagorean Identity

Answer 10

1/tan(x)
cos(x)/sin(x)

Question 11

tan(x) to what?

Pythagorean Identity

Answer 11

1/cot(x)
sin(x)/cos(x)

Question 12

sin(x) to what?

Pythagorean Identity

Answer 12

1/csc(x)

Question 13

Derivative of e^x

Answer 13

e^x

Question 14

Derivative of ln(x)

Answer 14

1/x

Question 15

sin²x to what?

Pythagorean Trigonometric Identity

Answer 15

1 - cos²x

Question 16

cos²x to what?

Pythagorean Trigonometric Identity

Answer 16

1 - sin²x

Question 17

tan²x to what?

Pythagorean Trigonometric Identity

Answer 17

sec²x - 1

Question 18

cot²x to what?

Pythagorean Trigonometric Identity

Answer 18

csc²x - 1

Question 19

sec²x to what?

Pythagorean Trigonometric Identity

Answer 19

tan²x + 1

Question 20

csc²x to what?

Pythagorean Trigonometric Identity

Answer 20

cot²x + 1

Question 21

Integral of kdx

Answer 21

kx + C

Question 22

Integral of sin(x)dx

Answer 22

-cos(x) + C

Question 23

Integral of cos(x)dx

Answer 23

sin(x) + C

Question 24

Integral of sec²(x)dx

Answer 24

tan(x) + C

Question 25

Integral of csc²(x)dx

Answer 25

-cot(x) + C

Question 26

Integral of sec(x)tan(x)dx

Answer 26

sec(x) + C

Question 27

Integral of csc(x)cot(x)dx

Answer 27

-csc(x) + C

Question 28

Integral of tan(x)dx

Answer 28

ln|sec(x)| + C

Question 29

Integral of cot(x)dx

Answer 29

ln|sin(x)| + C

Question 30

Integral of 1/(x² + a²) dx

Answer 30

(1/a)tan^-1(x/a) + C

Question 31

Integral of (1/sqrt(a² - x²)dx

Answer 31

sin^-1(x/a) + C
Where a > 0

Question 32

Integral of sinh(x)dx

Answer 32

cosh(x) + C

Question 33

Integral of cosh(x)dx

Answer 33

sinh(x) + C

Question 34

Integral of xⁿdx

Answer 34

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

Question 35

Integral of (1/x)dx

Answer 35

ln|x| + C

Question 36

Integral of e^xdx

Answer 36

e^x + C

Question 37

Integral of b^xdx

Answer 37

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

Question 38

Integral of -dx/(1-x²)

Answer 38

cos^{-1(x) + C}

Question 39

Integral of dx/(1 + x²)

Answer 39

tan^-1(x) + C

Question 40

Integral of sin(ax)dx

Answer 40

-cos(ax)/(a) + C

Question 41

Integral of cos(ax)dx

Answer 41

sin(ax)/(a) + C

Question 42

Integral of |x|dx

Answer 42

(x|x|)/2 + C