IB DP Maths: AA HL复习笔记5.2.2 Techniques of Differentiation
Chain Rule
What is the chain rule?
How do I know when to use the chain rule?
- The chain rule is used when we are trying to differentiate composite functions
- “function of a function”
How do I use the chain rule?
- “function of a function”
-
In trickier problems chain rule may have to be applied more than once
Are there any standard results for using chain rule?
- There are five general results that can be useful
Exam Tip
- You should aim to be able to spot and carry out the chain rule mentally (rather than use substitution)
- every time you use it, say it to yourself in your head
“differentiate the first function ignoring the second, then multiply by the derivative of the second function"
- every time you use it, say it to yourself in your head
Worked Example
Product Rule
What is the product rule?
How do I know when to use the product rule?
Exam Tip
Worked Example
Quotient Rule
What is the quotient rule?
Final answers should match the notation used throughout the question
How do I know when to use the quotient rule?
-
- if the numerator is a constant, negative powers can be used
- if the denominator is a constant, treat it as a factor of the expression
How do I use the quotient rule?
Exam Tip
Worked Example
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