IB DP Maths: AI 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?
How do I use the chain rule?
Are there any standard results for using chain rule?
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?
Final answers should match the notation used throughout the question
How do I know when to use the product rule?
- The product rule is used when we are trying to differentiate the product of two functions
- these can easily be confused with composite functions (see chain rule)
How do I use the product rule?
Exam Tip
Worked Example
Quotient Rule
What is the quotient rule?
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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