\[\left(\frac{\mathrm{d}}{\mathrm{d}z}\operatorname{nd}\left(z,k\right)\right)^{%
2}=\left({\operatorname{nd}}^{2}\left(z,k\right)-1\right)\left(1-{k^{\prime}}^%
{2}{\operatorname{nd}}^{2}\left(z,k\right)\right),\]