Chain Rule for Derivatives

Guided Notes for this lecture

In chapter one we reviewed composite functions. In this section we consider how to take the derivative of a composite functions called the chain rule. The way we think about this rule depends on what type of function the outside of the original composite function was. So we will do these in general first, then by type.

Derivatives of Polynomial and Power function types.

Derivatives of exponential types.

Derivatives of Natural Logarithm types

Derivative of Sine and Cosine types.

Derivatives with multiple chain rules.

At the end of this section you should be able to answer the following questions:

1. What are the key relationships between the chain rule and composite functions?
2. How can we determine what our "z" is for each chain rule??
3. How can we describe and write out the chain rule for a generic function?

Check Your Understanding
You should try these problems before reviewing the solutions to to these non-graded practice problems.