  In this paper we give full classification of rank 3 line arrangements in
$\mathbb P^2$ (over a field of characteristic 0) that have a minimal
logarithmic derivation of degree 3. The classification presents their defining
polynomials, up to a change of variables, with their corresponding affine
pictures. We also analyze the shape of such a logarithmic derivation, towards
obtaining criteria for a line arrangement to possess a cubic minimal
logarithmic derivation.
