Chain rule modules
After completing this section, students should be able to do the following.
- Recognize a composition of functions.
- Take derivatives of compositions of functions using the chain rule.
- Take derivatives that require the use of multiple rules of differentiation.
- Use the chain rule to calculate derivatives from a table of values.
- Understand rate of change when quantities are dependent upon each other.
- Use order of operations in situations requiring multiple rules of differentiation.
- Apply chain rule to relate quantities expressed with different units.
- Compute derivatives of trigonometric functions.
- Use multiple rules of differentiation to calculate derivatives from a table of values.
An unnoticed composition
Two young mathematicians discuss the chain rule.
The chain rule
Here we compute derivatives of compositions of functions.
Derivatives of trigonometric functions
We use the chain rule to unleash the derivatives of the trigonometric functions.