# Chain Rule Proof

## Homework Statement

If Z= F(x-y), show that Zx + Zy = 0

## The Attempt at a Solution

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

Fx(Q) * 1 + Fy(Q) * -1. By identity, this statement must hold for all values x,y. In particular, it must hold for x=y. By x=y,

Fy(Q) * 1 + Fy(Q) * -1 = 0.

Is this legitimate?

I'm not sure what you mean by Fx(Q) * 1 + Fy(Q) * -1. Are you differentiating F(Q) with respect to x and to y?

Deveno
F is just a real-valued function, it only has one derivative.

if Q(x,y) = x-y, then Q has 2 partials, Qx and Qy.

using the chain rule we get:

Zx = F'(Q)Qx