Derivada de Funciones Hiperbólicas Inversas

Siendo n una función derivable y n' su derivada.

$$f(x) = sin\:h^{-1} \: n \hspace{3em} f'(x) = \frac {n'}{\sqrt {n^2 + 1}}$$

$$f(x) = cos\:h^{-1} \: n \hspace{3em} f'(x) = \frac {n'}{\sqrt {n^2 - 1}}$$

$$f(x) = tan\:h^{-1} \: n \hspace{3em} f'(x) = \frac {n'}{1 - n^2}$$

$$f(x) = cot\:h^{-1} \: n \hspace{3em} f'(x) = \frac {n'}{1 - n^2}$$

$$f(x) = sec\:h^{-1} \: n \hspace{3em} f'(x) = \frac {- n'}{u \sqrt{1 - n^2}}$$

$$f(x) = csc\:h^{-1} \: n \hspace{3em} f'(x) = \frac {- n'}{|n| \sqrt{1 + n^2}}$$