Partial Derivative Questions

Hi i've attempted a few problems from my textbook which i've understood but i've come across 2 questions which have completly got my confused, and wouldnt mind some assistance :p.

1) Prove that if $z=2xy+x.f\frac{y}{x}$ then $x\frac{{\delta}z}{{\delta}x}+y\frac{{\delta}z}{{\d elta}y}=z+2xy$

2)If f=F(x,y) and $x=re^\theta$ , $y=re^{-\theta}$ prove that $2x\frac{{\delta}f}{{\delta}x}=r\frac{{\delta}f}{{\ delta}r}+{{\delta}f}{{\delta}\theta}$ and that $2y\frac{{\delta}f}{{\delta}y}=r\frac{{\delta}f}{{\ delta}r}-{{\delta}f}{{\delta}\theta}$

Quote:

Originally Posted by Kevlar

1) Prove that if $z=2xy+x.f\frac{y}{x}$

To me, this statement is unclear. What is f?

thats what i was wondering but heres a hard copy of the question :\

http://i50.tinypic.com/2jg6mib.png