Aloha :)
Partielle Ableitungen 1-ter Ordnung:$$f_x=\frac{\partial f}{\partial x}=\frac{10,84\cdot(-0,93)}{x^{1,93}\cdot y^{0,12}}$$$$f_y=\frac{\partial f}{\partial y}=\frac{10,84\cdot(-0,12)}{x^{0,93}\cdot y^{1,12}}$$
Partielle Ableitungen 2-ter Ordnung:$$f_{xx}=\frac{\partial^2 f}{\partial x^2}=\frac{10,84\cdot(-0,93)^2}{x^{2,93}\cdot y^{0,12}}$$$$f_{xy}=\frac{\partial^2 f}{\partial y\partial y}=\frac{10,84\cdot(-0,12)\cdot(-0,93)}{x^{1,93}\cdot y^{1,12}}=f_{yx}$$$$f_{yy}=\frac{\partial^2 f}{\partial y^2}=\frac{10,84\cdot(-0,12)^2}{x^{0,93}\cdot y^{2,12}}$$
Speziell an der Stelle \((x;y)=(4;1)\) lautet die Hesse-Matrix:$$H(4;1)\approx\left(\begin{array}{rr}0,33450 & 0,08331\\0,08331 & 0,40134\end{array}\right)$$
