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## Homework Statement

If Z= F(x-y), show that Z

_{x}+ Z

_{y}= 0

## Homework Equations

## The Attempt at a Solution

Suppose I let Q = x-y. Then, by chain rule,

F

_{x}(Q) * 1 + F

_{y}(Q) * -1. By identity, this statement must hold for all values x,y. In particular, it must hold for x=y. By x=y,

F

_{y}(Q) * 1 + F

_{y}(Q) * -1 = 0.

Is this legitimate?