4.3 Given that a ferromagnetic substance obeys Eq. (4.20), a) Show that the fractional change in the relative spontaneous magnetization produced per unit of applied field H is given by

\left(\frac{1}{\sigma_{s} / \sigma_{0}}\right) d\left(\frac{\sigma_{s}}{\sigma_{0}}\right)=\frac{\left(\mu_{H} / k T\right) d H}{\sinh u \cosh u-\left(T_{c} / T\right) \tanh u} where u=\frac{T_{c}}{T} \frac{\sigma_{s}}{\sigma_{0}}+\frac{\mu_{H} H}{k T}=\frac{T_{c}}{T} \frac{\sigma_{s}}{\sigma_{0}} if H is zero initially.