I am working on a data set with the Gaussian and the Student-t copulas and I need to define their derivatives.
For the Gaussian copula I have defined it as follows:
$$ \frac{d}{du}C^{Gauss}_{\alpha}= \Phi\Big(\frac{\Phi^{-1}(v)-\alpha\Phi^{-1}(u)}{\sqrt(1-\alpha^2)}\Big) $$ Where $C^{Gauss}_{\alpha}= \Phi_{\alpha}(\Phi^{-1}(u),\Phi^{-1}(v))$
However, I am having troubles defining the derivative w.r.t u of the Student-t distribution.
