To Explain: The chain rule formula is not simply the well-known rule for multiplying fractions.
Answer to Problem 66E
It has been explained why the chain rule formula is not simply the well-known rule for multiplying fractions.
Explanation of Solution
Given:
The chain rule formula:
Concept used:
Derivatives can be defined as follows:
Calculation:
The chain rule formula is given as,
This can be written as product of fractions as
However,
It may happen that a small change in
Note that this is not a concern for the terms in the chain rule, as each term is easily defined.
This is why the chain rule formula is not simply the well-known rule for multiplying fractions.
Conclusion:
It has been explained why the chain rule formula is not simply the well-known rule for multiplying fractions.
Chapter 3 Solutions
AP CALCULUS TEST PREP-WORKBOOK
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning