Science:Math Exam Resources/Courses/MATH100/December 2015/Question 02 (iv)
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Question 02 (iv) 

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 

What kind of differentiation rule can we apply? 
Hint 2 

Recall the chain rule : . 
Hint 3 

Can you write the given function as a composite function? 
Hint 4 

Recall that and . 
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. Let and . Then we can write the given function as a composite function :
By the chain rule (see Hint 2),
The final answer is D. 