Answer
$g_u=2ve^{2u/v}$
$g_v=-2ue^{2u/v}+2ve^{2u/v}$
Work Step by Step
Take the first partial derivatives of the given function. When taking partial derivative with respect to u, treat v as a constant, and vice versa:
$g_u=2/v\times v^2e^{2u/v}=2ve^{2u/v}$
$g_v=v^2e^{2u/v}\times -2u/v^2+2ve^{2u/v}=-2ue^{2u/v}+2ve^{2u/v}$
