MATH102 December 2010
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q1 (e) • Q1 (f) • Q2 (a) • Q2 (b) • Q2 (c) • Q2 (d) • Q3 • Q4 • Q5 • Q6 (a) • Q6 (b) • Q6 (c) • Q6 (d) • Q7 • Q8 • Q9 (a) • Q9 (b) • Q10 (a) • Q10 (b) • Q10 (c) •
Question 01 (c)
For this short-answer question, only the answers (placed in the boxes) will be marked.
Find the derivative of
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?
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!
You will need the chain rule, twice.
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We want to use the chain rule. So let the outer function ƒ(x) = x3 and the inner function g(x) = ln(x2+1). Then
In order to find the derivative of ln(x2+1) we use the chain rule again. So let's set h(x) = ln(x) and k(x) = x2+1. Then
Putting these results together we get our final answer:
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MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Chain rule