Verify that $f_{x y}=f_{y x}$ for the following function. \[ f(x, y)=e^{x+y+16} \] \[ \begin{array}{l} f_{x}=\square \\ f_{y}=\square \\ f_{x y}=f_{y x}= \end{array} \]

Step 1 ：Given the function \(f(x, y)=e^{x+y+16}\)

Step 2 ：Find the first order partial derivatives \(f_x\) and \(f_y\)

Step 3 ：\(f_x = e^{x+y+16}\)

Step 4 ：\(f_y = e^{x+y+16}\)

Step 5 ：Find the second order mixed partial derivatives \(f_{xy}\) and \(f_{yx}\)

Step 6 ：\(f_{xy} = e^{x+y+16}\)

Step 7 ：\(f_{yx} = e^{x+y+16}\)

Step 8 ：Since \(f_{xy} = f_{yx}\), we have verified the property for this function

Step 9 ：Final Answer: \(\boxed{f_{xy} = f_{yx} = e^{x+y+16}}\)