For 1, you multiplied correctly, but should simplify by combining the two x3 terms. When you differentiated, you have an error in the last term.
When you used the product rule, you differentiated incorrectly when you found u'. If u = 3 - x2, u' = -2x, not -2x-3 as you have. This is basically the same mistake that you made in the first part of this problem.
In 2, you only did this problem in one way - you didn't use the product rule. When you multiplied (x + 1/x) and (x - 1/x + 1) you have several mistakes. You ended up with two terms but there should be four.
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