Chain Rule (AQA A Level Maths): Revision Note
Exam code: 7357
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Chain Rule
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:
Examiner Tips and Tricks
The chain rule formulae are not in the exam formulae booklet – you have to know them.
When using the chain rule be sure to keep your functions straight (ie which function is y and which is u, or which is f and which is g).
Worked Example

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