Example of Partial Differentiation with Cobb-Douglas Production Function

The Cobb-Douglas Production Function (video 11:30) In this video, we are given the basic form of the Cobb-Douglas production function, we'll find the partial derivatives with respect to capital, K, and labor, L. Thereby finding the marginal products of capital and labor.

The Cobb-Douglas Production Function is typically written in a form something like, . Show that:                                 (what we are doing here is showing that the partial of a Cobb-Douglas Production function can be simplified in terms of P and the term the partial is in respect to, K in this case)

Given a basic Cobb-Douglas Production Function P, with Labour, L, Capital, K,  & a technology parameter A -- find the partial derivatives with respect to  K & L - and delivery the answer in a nice, handy solution in terms of P, L, K and/or A. Well - I wrote the problem in a rather confusing way -- so I'd suggest focusing instead on the steps toward the final solution.  Here is a basic Cobb-Douglas in terms of Capital, Labour and a technology parameter.          As a side note: here are a few alternate forms of the Cobb Douglas Production Function:       Now to the problem                   here we go                                                                               and since                                       & that's it.... Follow the same steps for  and you'll find that