Question 3 - A-Level Maths

$\quad y = \operatorname { arsinh } \left( \sqrt { x ^ { 2 } - 1 } \right) \quad x > 1$
1. Prove that $\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 1 } { \sqrt { x ^ { 2 } - 1 } }$
$$\mathrm { f } ( x ) = \frac { 1 } { 3 } \operatorname { arsinh } \left( \sqrt { x ^ { 2 } - 1 } \right) - \arctan x \quad x > 1$$
Determine the exact values of $x$ for which $\mathrm { f } ^ { \prime } ( x ) = 0$