022 Exam 2 Sample B, Problem 3

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Find the derivative of .


Foundations:  
This problem requires several advanced rules of differentiation. In particular, you need
The Chain Rule: If and are differentiable functions, then

    

The Product Rule: If and are differentiable functions, then

    
Additionally, we will need our power rule for differentiation:
for ,
as well as the derivative of the exponential function, :

 Solution:

Step 1:  
We need to start by identifying the two functions that are being multiplied together so we can apply the product rule.
and
Step 2:  
We can now apply the three advanced techniques.This allows us to see that

Final Answer:  

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