Science:Math Exam Resources/Courses/MATH110/December 2012/Question 03 (a)
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Question 03 (a) 

Calculate the following derivative. You may leave your answer unsimplified. , where , , and . 
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 

To take the derivative of you'll need the product rule. Remember that the derivative of is . 
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. We apply the product rule to to get:
Now we simply evaluate at x = 9, using the other information given in the problem to fill in g(9) and g'(9). Recall also that .
So the value of is . 