Science:Math Exam Resources/Courses/MATH110/April 2018/Question 01 (e)
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Question 01 (e) 

Find if . 
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 

Write and use the product 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 1 

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Please rate my easiness! It's quick and helps everyone guide their studies. Let . By the product rule, we know that so we just have to find .
Note that can be written as a composite of two functions: where and . By the chain rule with and , we have It follows that
We can use the doubleangle formula to simplify this further. We get Answer: The answer is . 
Solution 2 

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Please rate my easiness! It's quick and helps everyone guide their studies. We can write as a composite of two functions, To find , we apply the chain rule with . Then, we get By Solution 1, we have , so that the answer is . 