The purpose of the present paper is to introduce two novel subclasses $mathcal{T}_{mu}(n,{lambda},{alpha})$ and $mathcal{H}_{mu}(n,{lambda},{alpha};{kappa})$ of analytic and univalent functions with negative coefficients, involving Ruscheweyh derivative operator. The various results investigated in this paper include coefficient estimates, distortion inequalities, radii of close-to-convexity, starlikenes, and convexity for the functions belonging to the class $mathcal{T}_{mu}(n,{lambda},{alpha})$. These results are then appropriately applied to derive similar geometrical properties for the other class $mathcal{H}_{mu}(n,{lambda},{alpha};{kappa})$ of analytic and univalent functions. Relevant connections of these results with those in several earlier investigations are briefly indicated.