Use the Chain Rule to find the indicated partial derivatives.\\
$z = x^2 + xy^2$, $x = uv^3 + w^2$, $y = u + ve^w$\\
$\frac{\partial z}{\partial u}$, $\frac{\partial z}{\partial v}$, $\frac{\partial z}{\partial w}$ when $u = 2$, $v = 2$, $w = 0$\\
$\frac{\partial z}{\partial u} = $\\
$\frac{\partial z}{\partial v} = $\\
$\frac{\partial z}{\partial w} = $