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Partial derivative question

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I am taking a course by distance, and my professor provided an example of how to create a Hessian matrix using partial derivatives. He gave another example that just had the solution for us to try on our own.

I think that I am somehow not taking the second order partial derivative right. The attached file has the professors original example (solved step by step), his solved example and my work. Can you help me figure out where my mistake is?

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