Edexcel A Level Maths: Pure:复习笔记7.3.3 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: