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