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

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

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