Chain Rule (Edexcel International A Level Maths: Pure 3)

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:
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•  It allows us to differentiate functions that are not given in the form y= f(x):
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• There is a useful case which is used to integrate certain functions:
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