009A Sample Final 1, Problem 3

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Find the derivatives of the following functions.



For functions   and , recall
Chain Rule: 
Quotient Rule: 
Trig Derivatives: 



Step 1:  
Using the Chain Rule, we have

Step 2:  
Now, we need to calculate  
To do this, we use the Quotient Rule. So, we have


Step 1:  
Again, we need to use the Chain Rule. We have
Step 2:  
We need to calculate 
We use the Chain Rule again to get
Final Answer:  

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