022 Sample Final A, Problem 4

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Use implicit differentiation to find  

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
For this problem, we also need to use the product rule.


Step 1:  
First, we differentiate each term separately with respect to and apply the product rule on the right hand side to find that   differentiates implicitly to
Step 2:  
Now we need to solve for   , and doing so we find that  .
Final Answer:  

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