6 A Differentiation Product Rule KUS objectives BAT
6 A
Differentiation: Product Rule • KUS objectives BAT differentiate a product of two functions Starter: Differentiate
The Product Rule Example: The function y = x² (3 x - 9) can be written as where u = x² and v = 3 x – 9 y = uv,
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TRUE or FALSE ? You can't just differentiate each term and then multiply the results: Example: • When you differentiate the sum of two functions, you just eachifterm then add the results. differentiate We showed that you and differentiate y = When product of two functions, you just x² (3 xyou – 9)differentiate , you get 9 x²the – 18 x. differentiate each term and Differentiating x² gives 2 x. then multiply the results. Differentiating (3 x – 9) gives 3. Multiplying these together gives 2 x * 3 = 6 x This is not the same as 9 x² – 18 x
WORKING OUT SPACE (2 x + 1)2 is a common factor to both terms, so factorise
WORKING OUT SPACE Multiply the right by 2√(3 x-1) (Top and ‘Bottom’) so the denominators are the same
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Chili Pepper Challenge - MILD – write me an easy question for differentiation by product rule MEDIUM – now write a slightly trickier one HOT !!!– now a really tough one! Now swap questions
• KUS objectives BAT differentiate a product of two functions self-assess using: R / A / G ‘I am now able to ____. To improve I need to be able to ____’
- Slides: 12