Suppose $f$ is a differentiable function of $x$ and $y$, and $g(u, v) = f(e^u + \sin(v), e^u + \cos(v))$. Use the table of values below to calculate $g_u(0, 0)$ and $g_v(0, 0)$.
\begin{tabular}{|c|c|c|c|c|}
\hline
& $f$ & $g$ & $f_x$ & $f_y$ \\
\hline
(0, 0) & 5 & 6 & 2 & 3 \\
\hline
(1, 2) & 6 & 5 & 1 & 4 \\
\hline
\end{tabular}
$g_u(0, 0) = \underline{\hspace{2cm}}$
$g_v(0, 0) = \underline{\hspace{2cm}}$