Problem $10$: Show that

${\displaystyle \underset{V^{\text{'}}}{\overset{\phantom{}}{}}}\frac{M(r^{\text{'}})R}{R^3}d{V}^{\text{'}}={\displaystyle \underset{V^{\text{'}}}{\overset{\phantom{}}{}}}\frac{gra{d}^{\text{'}}M(r^{\text{'}})}{R}d{V}^{\text{'}}+o{\displaystyle \underset{S^{\text{'}}}{\overset{\phantom{}}{}}}\frac{M(r^{\text{'}})\text{h}\text{a}\text{t}(a{)}_{n^{\text{'}}}}{R}d{S}^{\text{'}},$

where $V^{\text{'}}$ is a region bounded by $S^{\text{'}},$ and hat$(a{)}_{n^{\text{'}}}$ is the unit normal to $S^{\text{'}}.$