Product Rule (CIE IGCSE Additional Maths)
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Maths
Product Rule
What is the product rule?
- The product rule is a formula that allows you to differentiate a product of two functions
- If where u and v are functions of x then the product rule is:
- In function notation, if then the product rule can be written as:
- The easiest way to remember the product rule is, for where u and v are functions of x:
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)
- is a composite function, “sin of cos of ”
- is a product, “sin x times cos ”
- These can easily be confused with composite functions (see chain rule)
How do I use the product rule?
- Make it clear what and are
- arranging them in a square can help
- opposite diagonals match up
- arranging them in a square can help
STEP 1
Identify the two functions, and
Differentiate both and with respect to to find and
STEP 2
Obtain by applying the product rule formula
Simplify the answer if straightforward to do so or if the question requires a particular form
Exam Tip
- The product rule formula is not on the list of formulas page – make sure you know it
- Don't confuse the product of two functions with a composite function:
- The product of two functions is two functions multiplied together
- A composite function is a function of a function
- To differentiate composite functions you need to use the chain rule
Worked example
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