Science:Math Exam Resources/Courses/MATH110/December 2011/Question 05 (c)
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Question 05 (c) 

Differentiate the following 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! 
Hint 

Watch out for the multiple use of the chain rule. 
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. Here we have several compositions going on. So a first step, would be to compute the derivative of We do this using the chain rule: Here we have that and And so: And so now, we can use the chain rule again to compute the derivative of Using: Where and we have And so we obtain 