inverse trig and hyperbolic derivatives

Question 1

d/dx (sin^-1(x)) =

Answer 1

1/√1-x²

Question 2

d/dx(cos^-1(x)) =

Answer 2

-1/√1-x²

Question 3

d/dx(tan^-1(x)) =

Answer 3

1/(1+x²)

Question 4

d/dx(csc^-1(x)) =

Answer 4

-1/(|x|√x²-1)

Question 5

d/dx(sec^-1(x)) =

Answer 5

1/(|x|√x²-1)

Question 6

d/dx(cot^-1(x)) =

Answer 6

-1/(1+x²)

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

sech^2(x)

Question 10

d/dx(coth(x)) =

Answer 10

-csch^2(x)

Question 11

d/dx(sech(x)) =

Answer 11

-sech(x)tanh(x)

Question 12

d/dx(csch(x)) =

Answer 12

-csch(x)coth(x)

Question 13

d/dx(sinh^-1(x))

Answer 13

1/√x²+1)

Question 14

d/dx(cosh^-1(x))

Answer 14

1/√x²-1)
x>1

Question 15

d/dx(tanh^-1(x))

Answer 15

1/(1-x²)
|x|<1

Question 16

d/dx(coth^-1(x))

Answer 16

1/(1-x²)
|x|>1

Question 17

d/dx(sech^-1(x))

Answer 17

-1/x√1-x²)
0<x<1

Question 18

d/dx(csch^-1(x))

Answer 18

-1/|x|√x²+1)
x not equal to 0