What is the chain rule?

• The chain rule is a formula that allows you to differentiate?composite functions
• If?y?is a function of?u, and?u?is a function of?x, then the?chain rule?tells us that:

• • ?Note that because?u?is a function of?x,?y?is also a function of?x

• In?function notation,?if ?then the chain rule can be written as:

This allows us to differentiate more complicated expressions:

What are the special cases of the chain rule?

• It allows us to differentiate a function raised to a power:

• ?It allows us to differentiate functions that are not given in the form?y=?f(x):

• There is a useful case which is used to integrate certain functions: