def dlogpdf_dlink_dvar(self, inv_link_f, y, Y_metadata=None):
e = y - inv_link_f<EOL>dlogpdf_dlink_dvar = (self.v*(self.v+<NUM_LIT:1>)*(-e))/((self.sigma2*self.v + e**<NUM_LIT:2>)**<NUM_LIT:2>)<EOL>return dlogpdf_dlink_dvar<EOL>
Derivative of the dlogpdf_dlink w.r.t variance parameter (t_noise)

.. math::
    \\frac{d}{d\\sigma^{2}}(\\frac{d \\ln p(y_{i}|\lambda(f_{i}))}{df}) = \\frac{-2\\sigma v(v + 1)(y_{i}-\lambda(f_{i}))}{(y_{i}-\lambda(f_{i}))^2 + \\sigma^2 v)^2}

:param inv_link_f: latent variables inv_link_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: derivative of likelihood evaluated at points f w.r.t variance parameter
:rtype: Nx1 array