\[f(x; y) = x^2y + 3x^2 + 4y - 5 \]
\[ f_x(x,y)= 2xy+6x \]
\[ f_y(x,y)= x^2+4 \]
\[ f_{xx}(x,y)= 2y+6 \]
\[ f_{yy}(x,y)= 0 \]
\[ f_{xy}(x,y)= 2x \]
\[ f_{yx}(x,y)= 2x \]