Aloha :)
Da Woframalpha offensichtlich Unsinn liefert:
$$\frac{\partial f}{\partial x}=104,16\cdot x^{-0,38}y^{0,28}\quad;\quad \frac{\partial f}{\partial x}=47,04\cdot x^{0,62}y^{-0,72}$$
$$\frac{\partial^2f}{\partial x^2}=-39,5808\cdot x^{-1,38}y^{0,28}\implies\frac{\partial^2f}{\partial x^2}(4,8;3,8)\approx-6,60254$$$$\frac{\partial^2f}{\partial x\partial y}=29,1648\cdot x^{-0,38}y^{-0,72}\implies\frac{\partial^2f}{\partial x\partial y}(4,8;3,8)\approx6,1453$$$$\frac{\partial^2f}{\partial y^2}=-33,8688\cdot x^{0,62}y^{-1,72}\implies\frac{\partial^2f}{\partial y^2}(4,8;3,8)\approx-9,0145$$
Die gesuchte Determinante lautet also:$$\begin{vmatrix}-6,60254 & 6,1453\\6,1453 & -9,0145\end{vmatrix}\approx21,7539$$
