If z=f(x,y), what's the differential of dx, dy, dz?

Question

This is an advanced calculus question, I just don't have an idea how to start with, pls help me out.

Answer 1

dz = (∂f(x,y)/∂x)dx+(∂f(x,y)/∂y)dy

**************************************

∂f(x,y)/∂x : consider y as a constant value and differential from x for example : ∂(5*x*y)/∂x=5*y
∂f(x,y)/∂y : consider x as a constant value and differential from y for example : ∂(5*x*y)/∂y=5*x

Answer 2

dz = (df/dx)dx + (df/dy)dy where the derivatives are partials. You can solve this for any of the three: dx, dy, dz.