z = xf(x + y) + yF(x + y)
f and F are arbitrary functions
Prove that zxx + zyy = 2zxy
(where xx and yy and xy are partial derivatives)
If someone could write up the proof, I would be grateful. My proof is exactly opposite of what I need. Every term on the left is exactly opposite of every term on the right. I get things like 2Fx on the left and 2fy on the right. I also get fxy and Fxy on the right and no terms like that on the left.
f and F are arbitrary functions
Prove that zxx + zyy = 2zxy
(where xx and yy and xy are partial derivatives)
If someone could write up the proof, I would be grateful. My proof is exactly opposite of what I need. Every term on the left is exactly opposite of every term on the right. I get things like 2Fx on the left and 2fy on the right. I also get fxy and Fxy on the right and no terms like that on the left.
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