MATH110 December 2013
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q2 • Q3 (a) • Q3 (b) • Q4 (a) • Q4 (b) • Q4 (c) • Q5 (a) • Q5 (b) • Q6 (a) • Q6 (b) • Q6 (c) • Q7 • Q8 • Q9 • Q10 (a) • Q10 (b) • QS01 10(a) • QS01 10(b) •
Question 03 (b)
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Rewrite in such a way that you can differentiate it using a different rule than the Power Rule. Name the rule of differentiation which is applicable, and then confirm that the derivative calculated using this alternative method is the same as in part (a).
(Bonus) You will receive one bonus mark for each different differentiation rule you use to differentiate .
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Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?
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If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!
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Hint
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There are lots of choices here. The easier ones to see are the chain rule, the definition of a derivative, and using logarithmic differentiation. There are of course many others as you will see in the solution.
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Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.
- If you are stuck on a problem: Read the solution slowly and as soon as you feel you could finish the problem on your own, hide it and work on the problem. Come back later to the solution if you are stuck or if you want to check your work.
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Solution
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Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies.
Parts b and c combined: (These are all the rules I can think of).
Addition rule:
Subtraction rule:
Product rule:
Quotient rule:
Chain rule:
Log-diff:
Exp-chain rule:
Limit definition of derivative:
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MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Chain rule, MER Tag Limit definition of the derivative, MER Tag Logarithmic differentiation, MER Tag Product rule, MER Tag Quotient rule, Pages using DynamicPageList3 parser function, Pages using DynamicPageList3 parser tag, Pages with math render errors
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