Problem

$y = \ln(\tanh 2x) \qquad x > 0$

(a) Show that

$$\frac{dy}{dx} = p\,\operatorname{cosech} 4x$$

where $p$ is a constant to be determined.

(b) Hence determine, in simplest form, the exact value of $x$ for which

$$\frac{dy}{dx} = 1.$$