Math 22 Partial Derivatives

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Partial Derivatives of a Function of Two Variables

 If , then the first partial derivatives of  with respect to  and  are the functions  and , defined as shown.
 
 
 
 
 
 We can denote  as  and  as 

Example: Find and of:

1)

Solution:  

2)

Solution:  

3)

Solution:  
(product rule +chain rule)

Higher-Order Partial Derivatives

1.

2.

3.

4.

1) , find

Solution:  
Then,

2) , find

Solution:  
Then,



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