We know that:
sinh–1 x = log(x + ),
cosh–1 x = log(x + ) and
tanh–1 x =
It can be proved that:
|i) (sinh–1 x) =||ii) (cosh–1 x) =|
|iii) (tanh–1 x) =||iv) (coth–1 x) =|
|v) (cosech–1 x) =||vi) (sech–1 x) =|
Did you note that the derivatives of tanh–1 x and coth–1 x are the same?
(Their domains are disjoint though).
Most of the times, the domain is not explicitly stated.
We find the derivative in its appropriate domain.