Prove that the \(\displaystyle sinh^{-1}x = ln(x+\sqrt{x^{2}+1}) \)

is \(\displaystyle sinh^{-1}x = \frac{1}{sinhx} \) ?

if so than could I write

\(\displaystyle sinh^{-1}x = \frac{2}{e^{x}-e^{-x}} \)

and am not sure how to got from there, any help appreciated.