Derive the continuity equation from first principles using an infinitesimal control volume of rectangular shape and having dimensions (dx, dy, dz). Identify the net mass flow rate through each surface of this element as well as the rate at which the mass of the element is increasing. The resulting equation should be expressed in terms of Cartesian coordinates (x, y, z, t), the Cartesian velocity components (u, v, w) and the fluid density?