022 Exam 1 Sample A, Problem 2

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2. Use implicit differentiation to find at the point on the curve defined by .

When we use implicit differentiation, we combine the chain rule with the fact that is a function of , and could really be written as Because of this, the derivative of with respect to requires the chain rule, so


Step 1:  
First, we differentiate each term separately with respect to to find that   differentiates implicitly to
Step 2:  
Since they don't ask for a general expression of , but rather a particular value at a particular point, we can plug in the values and  to find
which is equivalent to . This solves to
Final Answer:  

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