2 questions that aren't familiar to me...

1.

w(x,y) = f(u), where u = xy/(x^2 + y^2)

evaluate and simplify x dw/dx + y dw/dy

2.

Let f:R2 ->R be defined by f(x,y) = x^2 - 3y^2 and G:R2 ->R2 be defined by G(s,t) = {st,s+(t^2)}. Calculate Df,Dg and eventually D(f o G)(1,2).

and one that I can't remember the method for (not as important)...

3.

f(x,y) = xy / sqrt(x^2 + y^2), if (x,y) does not = (0,0), f(0,0) = 0

Prove the f is continuous at (0,0)