Calculus

Front 1

d/dx (uv)

Back 1

u'v + v'u

Hint 1

Product Rule

Front 2

d/dx (u/v)

Back 2

(u'v - v'u) / v²

Hint 2

Quotient Rule

Front 3

f(g(x))'

Back 3

f'(g(x)) g'(x)

Hint 3

Chain Rule

Front 4

d/dx c

Back 4

0

Front 5

d/dx x

Back 5

1

Front 6

d/dx cx

Back 6

c

Front 7

d/dx xⁿ

Back 7

nxⁿ ⁻ ¹

Front 8

d/dx eˣ

Back 8

eˣ

Front 9

d/dx aˣ

Back 9

aˣ ln|a|

Front 10

d/dx lnx

Back 10

1/x

Front 11

d/dx logₐx

Back 11

1 / (x lna)

Front 12

d/dx sinx

Back 12

cosx

Front 13

d/dx cosx

Back 13

-sinx

Front 14

d/dx tanx

Back 14

sec²x

Front 15

d/dx cotx

Back 15

-csc²x

Front 16

d/dx secx

Back 16

secx tanx

Front 17

d/dx cscx

Back 17

-cscx cotx

Front 18

d/dx arcsinx

Back 18

1 / √(1 - x²)

Front 19

d/dx arccosx

Back 19

-1 / √(1 - x²)

Front 20

d/dx arctanx

Back 20

1 / (1 + x²)

Front 21

d/dx arccotx

Back 21

-1 / (1 + x²)

Front 22

d/dx arcsecx

Back 22

1 / (|x| √(x² - 1))

Front 23

d/dx arccscx

Back 23

-1 / (|x| √(x² - 1))

Front 24

∫ dx

Back 24

x + C

Front 25

∫ xⁿdx

Back 25

xⁿ ⁺ ¹ / (n + 1) + C (n ≠ - 1)

Front 26

∫ dx/x

Back 26

lnx + C

Front 27

∫ eˣ dx

Back 27

eˣ + C

Front 28

∫ aˣ dx

Back 28

aˣ / (lna) + C

Front 29

∫ lnx dx

Back 29

x (lnx - 1) + C

Front 30

∫ sinx dx

Back 30

-cosx + C

Front 31

∫ cosx dx

Back 31

sinx + C

Front 32

∫ tanx dx

Back 32

-ln|cosx| + C

Front 33

∫ cotx dx

Back 33

ln|sinx| + C

Front 34

∫ secx dx

Back 34

ln|secx + tanx| + C

Front 35

∫ cscx dx

Back 35

-ln|cscx + cotx| + C

Front 36

∫ sec²x dx

Back 36

tanx + C

Front 37

∫ csc²x dx

Back 37

-cotx + C

Front 38

∫ secxtanx dx

Back 38

secx + C

Front 39

∫ cscxcotx dx

Back 39

-cscx + C

Front 40

∫ dx / √(a² - x²)

Back 40

arcsin(x / a) + C

Front 41

∫ dx / (a² + x²)

Back 41

arctan(x / a) + C

Front 42

∫ dx/(x √(x² - a²))

Back 42

arcsec(|x| / a) + C

Front 43

cscθ

Back 43

1 / sinθ

Hint 43

Reciprocal Identity

Front 44

secθ

Back 44

1 / cosθ

Hint 44

Reciprocal Identity

Front 45

cotθ

Back 45

1 / tanθ

Hint 45

Reciprocal Identity

Front 46

tanθ

Back 46

sinθ / cosθ

Hint 46

Quotient Identity

Front 47

cotθ

Back 47

cosθ / sinθ

Hint 47

Quotient Identity

Front 48

sin²θ + cos²θ

Back 48

1

Hint 48

Pythagorean Identity

Front 49

tan²θ + 1

Back 49

sec²θ

Hint 49

Pythagorean Identity

Front 50

1 + cot²θ

Back 50

csc²θ

Hint 50

Pythagorean Identity

Front 51

sin²(θ / 2)

Back 51

(1 - cosθ) / 2

Hint 51

Half-angle Formula

Front 52

cos²(θ / 2)

Back 52

(1 + cosθ) / 2

Hint 52

Half-angle Formula

Front 53

sin(2θ)

Back 53

2sinθcosθ

Hint 53

Double-angle Formula

Front 54

cos(2θ)

Back 54

cos²θ - sin²θ or

2cos²θ - 1 or

1 - 2sin²θ

Hint 54

Double-angle Formula