Derivative of Inverse Hyperbolic Functions

Question 1

Dx [sinh-1 x] =

Answer 1

1 / √(x^2 + 1)

Question 2

Dx [cosh-1 x] =

Answer 2

1 / √(x^2 – 1)

Question 3

Dx [tanh-1 x] =

Answer 3

1 / 1 – x^2, |x| < 1

Question 4

Dx [coth-1 x] =

Answer 4

1 / 1 – x^2, |x| > 1

Question 5

Dx [sech-1 x] =

Answer 5

-1 / x√(1-x^2)

Question 6

Dx [csch-1 x] =

Answer 6

-1 / |x|√(x^2 + 1)