Solution
= Solution
The <chain rule> gives $f_x=f_u u_x+f_v v_x$ and $f_y=f_u u_y+f_v v_y$. Since $u_x=2x$, $u_y=2y$, $v_x=2xy^2$ and $v_y=2x^2y$, the answer is
$$
\boxed{f_x=2xf_u+2xy^2f_v,\qquad f_y=2yf_u+2x^2yf_v.}
$$
Every <partial derivative> of $f$ on the right is evaluated at $u=1+x^2+y^2$, $v=1+x^2y^2$.