009A Sample Final 1, Problem 3

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Find the derivatives of the following functions.

a)

b)

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

Solution:

(a)

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

(b)

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:  
(a)
(b)

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