Problem

$$y = \operatorname{arsinh}x + \operatorname{arsinh}\left(\frac{1}{x}\right), \qquad x > 0$$

(a) Show that

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

(b) Hence determine the exact value of $y$ for which $\dfrac{dy}{dx} = 0$, giving your answer as a simplified natural logarithm.