022 Sample Final A, Problem 11

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Find the derivative:  .

(Note: You do not need to simplify the derivative after finding it.)

Foundations:  
This problem requires some more advanced rules of differentiation. In particular, it needs
The Chain Rule: If and are differentiable functions, then

    

The Quotient Rule: If and are differentiable functions and  , then

    

 Solution:

Find the derivative of the denominator:  
We need to use the chain rule, where the inner function is and the outer function is natural log:
Apply the Quotient Rule:  
Final Answer:  

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