Econ 11B Math for Economists - Example of Implicit Differentiation


Question 3 - Find the partial derivative 
 
of the implicit function, 
        
 


Implicit Function: we treat z as a function of x & y
And in finding 
, we treat x as constant. 


    

Remember, we treat .z as a function of y. You could also think of  as

Also note that in an implicit partial differentiation we consider x as a constant, thus .



        
                    We now solve for 




        
                    our answer, 


Also, here are some more correct, alternative forms;
                       


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