In this letter, cosmology of a simple NMDC gravity with ξRφ,µφ ,µ term and a free kinetic term is considered in flat geometry and in presence of dust matter. A logarithm field transformation φ ′ = µ ln φ is proposed phenomenologically. Assuming slow-roll approximation, equation of motion, scalar field solution and potential are derived as function of kinematic variables. The field solution and potential are found straightforwardly for power-law, de-Sitter and super-acceleration expansions. Slow-roll parameters and slow-roll condition are found to depend on more than one variable. At large field the re-scaling effect can enhance the acceleration. For slow-rolling field, the negative coupling ξ could enhance the effect of acceleration. * buring@nu.ac.th †