Homogeneous function of degree n

[athrun200]

Homework Statement

See photo

Homework Equations

The Attempt at a Solution

I am learning partial differential and never be taught about homongeneous function.
What is this? How to solve the problem?

 

[athrun200]

I finally figure out how to do part a.
See my work on the photo.

Part b is similar to part a except 1 step.
That is, I need to prove $f_{xy}$=$f_{yx}$

It seems the question doesn't provide enough equation for me to do this.