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