Smoothness of Surfaces in $\Bbb R^4$

Question

Let $U=\{(x,y,z): x>0,y>0,z>0\}$ be the first octant, and let $g:U\to\Bbb R^4$ be given by $g(t,u,v)=(tu,tv,uv,tuv)$. Determine whether the image of g defines a smooth surface. I know how to determine whether a surface in $\Bbb R^3$ is smooth or not, but waht about the surface $\Bbb R^4$?