Additional Resources
OpenStax Online Textbook
How to Read a Math Textbook
Additional Instructional Resources
Chain Rule- DS3
Objectives
- State the chain rule for the composition of two functions.
- Apply the chain rule together with the power rule.
- Apply the chain rule and the product/quotient rules correctly in combination when both are necessary.
- Recognize the chain rule for a composition of three or more functions.
- Describe the proof of the chain rule.
Summary
A composite function is one where the input variable first passes through one function, and then the resulting output passes through another. For example, the function is composite since
Given a composite function where and are differentiable functions, the chain rule tells us that