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Consider the curve defined by .
(a) Find as a function of and . Your answer does not need to be in its most simplified form, but you do need to solve for explicitly in terms of and .
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.
Simplify the equation. is the inverse of .
Use implicit differentiation and remember chain rule.
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.
Applying on both sides of the equation, we can implicitly differentiate . Then by applying product rule and chain rule we get