Question

For d2f/(dxdy), do we take the derivate of f with respect to y first, or with respect to x first? For fxy, do we take the derivate of f with respect to y first, or with respect to x first?

Answer 1

For d2f/dxdy, it's the same as d/dx(df/dy) so take the derivative of f with respect to y first. For the second one, fxy, take derivative w.r.t. x first.

Answer 2

IT DOES NOT MATTER GO LOOK AT BERNOULLIS PROOF OF PARtial derivitives

Answer 3

They are the same.

Answer 4

They are not quite the same. Just remember the assumptions in the proof that \[f_{xy} = f_{yx}\]Don't just memorise the formulas when doing your applications but forget the full statement of the theorem.