I'm not sure how far back you need to go. However, if you look at 4.3.16a and go from there, the authors claim that

This is most definitely true if it is known that

is bounded.

is called the stream function. If it represents a physical parameter, then most likely you can assume

is bounded on physical grounds. The same goes for

itself. But now, if

and

are both bounded, then it is the case that

.

The authors also claim that

goes to

as

goes to infinity. If that is the case, then if you take limits in the entire Equation 4.3.16a, you will get

on the LHS, which implies you must get

on the RHS. Hence,

. Multiplying through by

gives you Equation 4.3.16b.

So, in getting 4.3.16b from 4.3.16a, the problem reduces down to knowing that

and

are both bounded, and that

.

With regard to the second derivative, you might be able to get that from the "note" in-between Equations 4.3.10 and 4.3.11: "... noting that

..." This tells you that

, and hence

. Is it the case that

?

These are just the beginnings of some ideas.