Find $f_{x x}, f_{x y}, f_{y x}$ and $f_{y y}$ for the following function. (Remember, $f_{y x}$ means to differentiate with respect to $y$ and then with respect to $x$.) \[ f(x, y)=9 y \ln x \] \[ \mathrm{f}_{\mathrm{xox}}=\square \]

Step 1 ：First, we find the first order partial derivatives of the function \(f(x, y)=9y \ln x\).

Step 2 ：We find that \(f_x = \frac{9y}{x}\) and \(f_y = 9\ln x\).

Step 3 ：Next, we differentiate \(f_x\) with respect to \(x\) to get \(f_{xx}\), and we find that \(f_{xx} = -\frac{9y}{x^2}\).

Step 4 ：We then differentiate \(f_x\) with respect to \(y\) to get \(f_{xy}\), and we find that \(f_{xy} = \frac{9}{x}\).

Step 5 ：We differentiate \(f_y\) with respect to \(x\) to get \(f_{yx}\), and we find that \(f_{yx} = \frac{9}{x}\).

Step 6 ：Finally, we differentiate \(f_y\) with respect to \(y\) to get \(f_{yy}\), and we find that \(f_{yy} = 0\).

Step 7 ：\(\boxed{f_{xx} = -\frac{9y}{x^2}, f_{xy} = \frac{9}{x}, f_{yx} = \frac{9}{x}, f_{yy} = 0}\)