Hyperbolic Functions Formula

Question 1

sinh(x)

Answer 1

eˣ - e⁻ˣ/2

Question 2

cosh(x)

Answer 2

eˣ + e⁻ˣ/2

Question 3

tanh(x)

Answer 3

sinh(x)/cosh(x) = [eˣ - e⁻ˣ] / [eˣ + e⁻ˣ] or [e²ˣ -1] / [e²ˣ +1]

Question 4

cosech(x)

Answer 4

2/eˣ - e⁻ˣ

Question 5

sech(x)

Answer 5

2/eˣ + e⁻ˣ

Question 6

coth(x)

Answer 6

cosh(x)/sinh(x) = [eˣ + e⁻ˣ] / [eˣ - e⁻ˣ] or [e²ˣ +1] / [e²ˣ -1]

Question 7

d/dx sinh(x)

Answer 7

cosh(x)

Question 8

d/dx cosh(x)

Answer 8

sinh(x)

Question 9

d/dx tanh(x)

Answer 9

sech²(x)

Question 10

d/dx cosech(x)

Answer 10

-cosech(x) ⋅ coth(x)

Question 11

d/dx sech(x)

Answer 11

-sech(x) ⋅ tanh(x)

Question 12

d/dx coth(x)

Answer 12

-cosech²(x)

Question 13

cosh²(x) - sinh²(x)

Answer 13

1

Question 14

tanh²(x) + sech²(x)

Answer 14

1

Question 15

coth²(x) - cosech²(x)

Answer 15

1

Question 16

sinh(x ± y)

Answer 16

sinh(x) ⋅ cosh(y) ± sinh(y) ⋅ cosh(x)

Question 17

cosh(x ± y)

Answer 17

cosh(x) ⋅ cosh(y) ± sinh(x) ⋅ sinh(y)

Question 18

sinh(2x)

Answer 18

2[sinh(x) ⋅ cosh(x)]

Question 19

cosh(2x)

Answer 19

cosh²(x) ⋅ sinh²(x)

Question 20

sinh²(x)

Answer 20

[cosh(2x) - 1] /2

Question 21

cosh²(x)

Answer 21

[cosh(2x) + 1] /2

Question 22

sinh⁻¹(x)

Answer 22

ln |x + C|

Question 23

cosh⁻¹(x)

Answer 23

ln |x + √(x² - 1)|

Question 24

tanh⁻¹(x)

Answer 24

1/2ln |(1 + x) / (1 - x)|

Question 25

cosech⁻¹(x)

Answer 25

1/2ln |(x + 1) / (x - 1)|

Question 26

sech⁻¹(x)

Answer 26

ln |{1 + √(1 - x²)} / x|

Question 27

coth⁻¹(x)

Answer 27

ln |1/x + √(1 - x²) / |x||

Question 28

d/dx sinh⁻¹(x)

Answer 28

1/√(x² + 1)

Question 29

d/dx cosh⁻¹(x)

Answer 29

1/√(x² - 1)

Question 30

d/dx tanh⁻¹(x)

Answer 30

1 / (1 - x²)

Question 31

d/dx cosech⁻¹(x)

Answer 31

-1 / [|x|√(1 + x²)]

Question 32

d/dx sech⁻¹(x)

Answer 32

-1 / [x√(1 - x²)]

Question 33

d/dx coth⁻¹(x)

Answer 33

1 / (1 - x²)