Science:Math Exam Resources/Courses/MATH102/December 2012/Question C 02
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Question C 02 

Use the definition of the derivative to calculate the derivative of The following might be a useful fact in simplifying the limit: . 
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 

The definition of the derivative 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. Using the definition of the derivative from the hint, we set up:
Now we use the hint from the statement of the question. If we multiply by a conjugate, we can move the square roots and make our limit easier to solve.
