# Partial Derivatives

1. Dec 31, 2007

### jesuslovesu

[SOLVED] Partial Derivatives

Whoops, never mind my calculus book explained it.

1. The problem statement, all variables and given/known data
F(x,y,z) = 0
$$(\frac{\partial x}{\partial y})\right)_{z} (\frac{\partial y}{\partial x})\right)_{z}$$ = 0

Show
$$(\frac{\partial x}{\partial y})\right)_{z} (\frac{\partial y}{\partial z})\right)_{x} (\frac{\partial z}{\partial x})\right)_{y}$$ = -1

3. The attempt at a solution

Well I drew out a diagram
F
dF/dx dF/dy dF/dz

dx/dy dx/dz dy/dx dy/dz dz/dx dz/dy

So I would assume that the reason the second expression is = -1 because of the chain rule, however, I really don't see why it would be -1...
If it were dx/dy dy/dx dz/dx would it be 1? Just because the middle term is dy/dz the sign will change?

Last edited: Dec 31, 2007