Question

Session 42: In answer to question 3 given in the problem set (PDF), can someone please explain me why z is equalled to zero for the first two differentials (dx, and dy) and is not changed in case of dz. I am really confused here.

Answer 1

The only thing I can think of is the question meant to ask for
\[ \frac{\partial w}{\partial x}\bigg|_{z=0} \]
and they did not bother with the last dz term, because all they wanted was the "coefficient" of the dx term

Answer 2

I think the question is a bit faulty- they also say \[dy = \frac{ 2xy + y^{2} }{x ^{2} + 2xy} dx\] when it should be negative: \[dy = -\frac{ 2xy + y^{2} }{x ^{2} + 2xy} dx\]
I'm not sure where the z = 0 came from either.