How did the book get to (7.12)?

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SUMMARY

The discussion centers on the application of the multivariable chain rule in calculus, specifically in relation to problem 7.12. The user successfully identified terms 1, 3, 5, and 7 through the FOIL method but expressed confusion regarding the derivation of terms 2, 4, and 6. Key concepts highlighted include the importance of the product rule and the non-commutativity of operators in this context.

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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



4jmjyxo.jpg


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?
 
Physics news on Phys.org
Don't forget the product rule; 1/r is a function of r, and c and s are functions of θ.
 

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