code: def dlogpdf_dlink(self, inv_link_f, y, Y_metadata=None):
          
          e = y - inv_link_f
          grad = ((self.v + 1) * e) / (self.v * self.sigma2 + (e**2))
          return grad
docs: Gradient of the log likelihood function at y, given link(f) w.r.t link(f)
  
          .. math::
              \\frac{d \\ln p(y_{i}|\lambda(f_{i}))}{d\\lambda(f)} = \\frac{(v+1)(y_{i}-\lambda(f_{i}))}{(y_{i}-\lambda(f_{i}))^{2} + \\sigma^{2}v}
  
          :param inv_link_f: latent variables (f)
          :type inv_link_f: Nx1 array
          :param y: data
          :type y: Nx1 array
          :param Y_metadata: Y_metadata which is not used in student t distribution
          :returns: gradient of likelihood evaluated at points
          :rtype: Nx1 array