def dlogpdf_dlink(self, inv_link_f, y, Y_metadata=None):
e = y - inv_link_f<EOL>grad = ((self.v + <NUM_LIT:1>) * e) / (self.v * self.sigma2 + (e**<NUM_LIT:2>))<EOL>return grad<EOL>
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