Find $f_{x y}$ when \[ f(x, y)=(2 x-y) e^{x y} . \] 1. \[ f_{x y}=(2+x y)(2 x-y) e^{x y} \] 2. \[ f_{x y}=(1+x y)(2 x-y) e^{x y} \] 3. \[ f_{x y}=(2-x y)(2 x-y) e^{x y} \] 4. $f_{x y}=(1+x y) e^{x y}$ 5. $f_{x y}=(1-x y) e^{x y}$ ×6. $f_{x y}=(2+x y) e^{x y}$

Step 1 ：Take the partial derivative of \(f\) with respect to \(x\):

Step 2 ：\(f_{x} = (2x - y) e^{xy} + (2x - y) y e^{xy}\)

Step 3 ：Take the partial derivative of \(f_{x}\) with respect to \(y\):

Step 4 ：\(f_{xy} = (2x - y) x e^{xy} + (2x - y) e^{xy} + 2 e^{xy} - y e^{xy}\)

Step 5 ：Simplify the expression:

Step 6 ：\(f_{xy} = (1 + xy)(2x - y) e^{xy}\)

Step 7 ：Final Answer: \(\boxed{f_{xy} = (1 + xy)(2x - y) e^{xy}}\)