Higher Order Partial Derivatives and Clairaut's Theorem

[ChiralWaltz]

Homework Statement

general course question

Homework Equations

N/A

The Attempt at a Solution

f_x is a first order partial derivative
f_xy is a second order partial derivative
f_xyz is a third order partial derivative

I understand that Clairaut's Theorem applies to second order derivatives, does it also apply to higher partial derivatives though?

Example:
f_xy=f_yx (Clairaut's)

So does this apply?
f_xyz=f_xzy=f_zyx

 

[SqueeSpleen]

Yes it applies.
(1) f_xy=f_yx (Clairaut's)
We know that:
f_xyz=(f_x)_yz
How can you prove that:
f_xyz=f_xzy using that?