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Partial Differentiation

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Can someone show me in a step-by-step way how the following partial differentiations were obtained?

the-differentiation-problem.jpg

I assume that you can differentiate Y with respect to L and get a dY/DL as a function of L and K.

 

Then the tricky part is getting rid of the term in the square bracket. Express the term in the square bracket as a function of Y and alpha. Then substitute the expression you get for the term in the sqare bracket into your solution for DY/DL.

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