022 Exam 2 Sample B, Problem 3

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Find the derivative of .

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, :


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

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