Chain Rule

How to differentiate composite functions?

You need to learn the chain rule to differentiate functions of other functions, or composite functions:

Note: Make sure you can identify what u is in the expression given, which may require to rewrite the orginal expression given.

Example 1:

This formula can also be written in function notation:

Example 2:

Note: For the chain rule, you could use any of the two formulas.

It is possible to differentiate expressions not in the form of f(x):

Note: This formula is a case of the chain rule. You could rewrite the formula into this form:

Example 3:

Practice Question:

Show Answer

Note: Ensure you are solid with the chain rule, as typically in exam questions, this will be paired with the product rule and the quotient rule, which are concepts later on this chapter.