How did the book get to (7.12)?

[TheFerruccio]

Homework Statement

I am reading through a chapter on the multivariable chain rule, and I was able to follow the steps up until 7.12. It is photographed below.

Homework Equations

The Attempt at a Solution

Of the terms listed, I am able to FOIL the operators out, understanding that, because the statement has operators, that commutativity is not necessarily true. From this, I was able to get, of the 7 terms listed in 7.12, terms 1, 3, 5, 7. I do not know where they get terms 2, 4, 6 from.

What am I missing in my multiplication of operators?

 

[gopher_p]

Don't forget the product rule; 1/r is a function of r, and c and s are functions of θ.