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Chain Rule (Edexcel International A Level Maths: Pure 3)
Revision Note
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:
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- 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 Tip
- 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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