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. $f_{x y}=(2+x y) e^{x y}$

Answer

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Answer

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

Steps

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