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