$4\mathrm{.}8$ Derive the expressions given in Tables $4\mathrm{.}4$ and $4\mathrm{.}5$ for the derivatives $x_q,M_w,Y_p,N_v.$

Table $4\mathrm{.}4$

Longitudinal Dimensional Derivatives

Table $4\mathrm{.}5$

Lateral Dimensional Derivatives