Science:Math Exam Resources/Courses/MATH110/December 2013/Question 06 (b)
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Question 06 (b) 

Consider the function: (b) 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 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 

Simplify the function first as was done in part (a) and then use the chain rule. 
Hint 2 

You can also differentiate this using logarithmic differentiation. 
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 1 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. Since we have simplified, we can simply apply the chain rule to it using .
Combining, we get:

Solution 2 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. Alternatively, we can start with the initial function and use logdiff:
