Science:Math Exam Resources/Courses/MATH100/December 2015/Question 03 (ii)
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Question 03 (ii) 

Let . Find at the point (1,1). 
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 

Try to use implicit differentiation. 
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. As we mention in the Hint, here we use the method of implicit differentiation. First differentiate both side of the given equation :
Plugging back these and solving the equation for ,
and hence
Finally, by plugging , we have
Therefore, the final answer is A. 