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Question 02 

Let . Use the definition of derivative to find . No marks will be given for the use of any differentiation rules. 
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 

There are two equivalent limit definitions of the derivative at the point : and given that these limits exist. You can use either definition. See Solution 1 for the former approach, and Solution 2 for the latter. 
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. Here we first calculate the derivative for any value and only then plug in the value . That is, we first calculate We use this to evaluate the derivative of the given function:
Lastly, plugging in we obtain . 
Solution 2 

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Please rate my easiness! It's quick and helps everyone guide their studies. In this solution we use the formula
We could calculate for any value of and then plug in , as it was done in Solution 1, but to show an alternative we plug in directly. Following the above definition of the derivative and the definition of the function we obtain:
