Difference between revisions of "Math 22 Partial Derivatives"

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Latest revision as of 16:21, 3 September 2020

Partial Derivatives of a Function of Two Variables

 If Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z=f(x,y)}
, 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 , given that ,

Solution:  
Then,

2) Find , given that ,

Solution:  
Then,



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