(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If Z= F(x-y), show that Z_{x}+ Z_{y}= 0

2. Relevant equations

3. 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?

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# Homework Help: Chain Rule Proof

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