Science:Math Exam Resources/Courses/MATH100/December 2015/Question 03 (iii)
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Question 03 (iii) 

Let . What is ? (Remember .) 
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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

Can you find the derivative of ? (Using one of the log rules, rewrite . Then compute the derivative.) 
Hint 2 

WHat is the differentiation rule to find ? 
Checking a solution serves two purposes: helping you if, after having used all the hints, 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. By the chain rule, and hence . Now let's find . By the log rule , so can be written as . Taking the derivative on both side and using the product rule, . Therefore, we have . The final answer is E. 