Science:Math Exam Resources/Courses/MATH110/December 2010/Question 04 (b)
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Question 04 (b) 

Given a differentiable function , recall that there are two definitions for : and Use one of the definitions given to find the derivative of the function at . 
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 

Finding the derivative of at is the same as finding . 
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. We are trying to find where and . Using the first definition of the derivative, we need to know which we calculate here:
Plugging this, and into the definition of the derivative, we get:

Solution 2 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. We are trying to find where and . Using the second definition of the derivative, we will need to know and . Since , they are as follows:
Plugging these into our definition we get:
