1. Partial derivatives

I don't seem to understand the function here

2. just use the chain rule:

$
\begin{gathered}
f_x = g_u u_x + g_v v_x + g_w w_x \hfill \\
f_y = g_u u_y + g_v v_y + g_w w_y \hfill \\
\end{gathered}
$