Question 7 - A-Level Maths

Given that $y = \ln \tanh \frac { x } { 2 }$, where $x > 0$, show that $$\frac { \mathrm { d } y } { \mathrm {~d} x } = \operatorname { cosech } x$$
A curve has equation $y = \ln \tanh \frac { x } { 2 }$, where $x > 0$. The length of the arc of the curve between the points where $x = 1$ and $x = 2$ is denoted by $s$.
1. Show that $$s = \int _ { 1 } ^ { 2 } \operatorname { coth } x \mathrm {~d} x$$
2. Hence show that $s = \ln ( 2 \cosh 1 )$.