Problem

$$y=\operatorname{arsinh}\left(\sqrt{x^2-1}\right)\qquad x>1$$

(a) Prove that

$$\frac{dy}{dx}=\frac{1}{\sqrt{x^2-1}}$$

(b) Determine the exact values of $x$ for which $f'(x)=0$, where

$$f(x)=\frac13\operatorname{arsinh}\left(\sqrt{x^2-1}\right)-\arctan x \qquad x>1$$