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