022 Sample Final A, Problem 8
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Find ther marginal productivity of labor and marginal productivity of capital for the following CobbDouglas production function:
(Note: You must simplify so your solution does not contain negative exponents.)
Foundations: 

The word 'marginal' should make you immediately think of a derivative. In this case, the marginal is just the partial derivative with respect to a particular variable. 
The teacher has also added the additional restriction that you should not leave your answer with negative exponents. 
Solution:
Marginal productivity of labor: 

we take the partial derivative with respect to : 

Marginal productivity of capital: 

Now, we take the partial derivative with respect to : 

Final Answer: 

Marginal productivity of labor:

Marginal productivity of capital:
