MATH104 December 2012
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q1 (e) • Q1 (f) • Q1 (g) • Q1 (h) • Q1 (i) • Q1 (j) • Q1 (k) • Q1 (l) • Q1 (m) • Q1 (n) • Q1 (o) • Q2 (a) • Q2 (b) • Q2 (c) • Q2 (d) • Q2 (e) • Q3 • Q4 (a) • Q4 (b) • Q4 (c) • Q5 (a) • Q5 (b) • Q6 (a) • Q6 (b) • Q6 (c) • Q6 (d) •
Question 01 (n)
Find the derivative of the function
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!
We need the chain rule for this problem and might need to use it more than once. Can you identify an inner and outer function for ?
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This question requires multiple uses of the chain rule.
Recognizing that the inner function is and the outer function is , we apply the chain rule and get
Now we need to use the chain rule again to evaluate . The function has inner function and outer function . Thus, is given by
Thus putting the pieces together, we write the expression for the derivative of :
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