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Differential Calculus for the Life Sciences (Edelstein-Keshet)
9: Chain Rule Applied to Related Rates and Implicit Differentiation

9: Chain Rule Applied to Related Rates and Implicit Differentiation

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Jun 21, 2023
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- 8.4: Exercises
- 9.1: Applications of the Chain Rule to “Related Rates”

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9.1: Applications of the Chain Rule to “Related Rates”
In many applications of the chain rule, we are interested in processes that take place over time. We ask how the relationships between certain geometric (or physical) variables affects the rates at which they change over time. Many of these examples are given as word problems, and we must assemble the required relationships to solve the problem.
9.2: Implicit Differentiation
Implicit differentiation makes use of the chain rule to differentiate implicitly defined functions.
9.3: The Power Rule for Fractional Powers
Implicit differentiation is a useful technique for finding derivatives of inverse functions. This general idea recurs in later chapters when we introduce new functions and their inverses.
9.4: Summary
9.5: Exercises

Thumbnail: Chain. (Unsplash license; Miltiadis Fragkidis via Unsplash)

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