Given that, $\displaystyle sinh \ y = x $, show that $\displaystyle y = ln [x+(1+x^2)^\frac{1}{2}] $

By differentiating this result, show that

$\displaystyle (1+x^2)(\frac {dy}{dx})^2 = 1$

I’ve done first part, but how can I differentiating this result?