Vector field divergence equivalent definition

Could someone direct me to a proof showing the equivalence between the following two definitions of the divergence of vector field $F$ at $x$? (1) $lim_{|V| to 0} cfrac{alpha({S})}{|V|}$, where $alpha$ is the surface integral of $F$ over surface $S$ with volume $V$ containing $x$ (2) $cfrac{partial F_1}{partial x_1} + dots + cfrac{partial F_n}{partial x_n}$; the first makes intuitive sense to me, the second not at all.