Science:Math Exam Resources/Courses/MATH100/December 2016/Question 09 (b) (i)
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Question 09 (b) (i) 

Let . (i) Compute and simplify . 
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! 
Hint 

Use the quotient rule, or logarithmic differentiation. 
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.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. We find on Note that on this set, is welldefined and doesn't vanishes. (i.e., .) To do so, we use logarithmic differentiation. For this purpose, define by . Then, its derivative can be easily calculated, and is given by . On the other hand, by the chain rule, relates with in the following way:
Hence for any . 