Funktionen:

\[
f(x,y) = \frac{-(x^2-1)(y^2-4)-x^2-y^2+5}{(x^2+y^2+1)^2}
\]

Partialderivata 1:

\[
f_1 =\frac{2 x (- 3 x^2 + 2 y^2 -y^4 + x^2 y^2 + 1)}{( x^2 + y^2 + 1)^3}
\]

Partialderivata 2:

\[
f_2 = \frac{2 y (-7 x^2-x^4+x^2 y^2-2)}{(x^2+y^2+1)^3}
\]