  We compute the fourth order action in perturbation theory for scalar and
second order tensor perturbations for a minimally coupled single field
inflationary model, where the inflaton's lagrangian is a general function of
the field's value and its kinetic energy. We obtain the fourth order action in
two gauges, the comoving gauge and the uniform curvature gauge. Using the
comoving gauge action we calculate the trispectrum at leading order in
slow-roll, finding agreement with a previously known result in the literature.
We point out that in general to obtain the correct leading order trispectrum
one cannot ignore second order tensor perturbations as previously done by
others. The next-to-leading order corrections may become detectable depending
on the shape and we provide the necessary formalism to calculate them.
