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