You can look at this term by term to make things simpler. I'll do the first couple of terms to start things off:

x^{2}

The differential of this term is fairly easy since it involves only one variable. I like to think of a differential this way. You know the derivative (dz/dx) of z = x^{2}:

(dz/dx) = 2x

Well, if you treat the derivative like a fraction, and multiply through by dx, you get:

dz = 2x dx

which is the differential of x^{2}.

-2xy

This term is a more difficult term. Here you have to make use of the product rule:

d(uv) = u dv + v du

So in this case,

d(-2xy) = -2 d(xy) = -2(xdy + ydx) = -2x dy - 2y dx

You should be able to do the rest now.