Funktionen

\[ f[x,y]=((1-x^2)*(y^2 -4)- x^2 -y^2 +5)/(x^2 +y^2 +1)^2 \]

Derivatan map x

\[ \frac{-2 x \left(y^2-4\right)-2 x}{\left(x^2+y^2+1\right)^2}-\frac{4 x \left(\left(1-x^2\right) \left(y^2-4\right)-x^2-y^2+5\right)}{\left(x^2+y^2+1\right)^3} \]

Derivatan map y

\[ \frac{2 \left(1-x^2\right) y-2 y}{\left(x^2+y^2+1\right)^2}-\frac{4 y \left(\left(1-x^2\right) \left(y^2-4\right)-x^2-y^2+5\right)}{\left(x^2+y^2+1\right)^3} \]