Science:Math Exam Resources/Courses/MATH102/December 2015/Question 03
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Question 03 

Let be the inverse function of . Assume that and . Find the tangent line to at . (a) (b) (c) (d) (e) 
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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

We do not have an algebraic expression for . When we want to find the derivative of a function that is not defined by a simple algebraic formula, we should try to use implicit differentiation. 
Hint 2 

Following the first hint, we will try to set this equation up for implicit differentiation.
Let

Checking a solution serves two purposes: helping you if, after having used all the hints, 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. In order to solve this problem, we use implicit differentiation. 