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Higher Mathematics —— Higher-order Derivative Problem
Principle: The whole formula is regarded as the multiplication of n+ 1 brackets, where x and -k are added.

When expanding, it is regarded as taking either X or -k from each bracket for multiplication.

Specific to this problem: the first term is easy to get, and the n+ 1 power of x can only be taken in each bracket.

The second item is not difficult either. Take a number in parentheses instead of x at a time, and then add these n expressions about x to the n power.

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Starting from the third item is more difficult, but the reason is the same.

From the above analysis, we know that the original formula is a polynomial of x's k power, and the expanded part is enough for us to do the problem, because the latter part will be equal to 0 after taking the derivative of n+ 1, except for the first term.

Therefore, only the derivative of the first term is needed. The first term of n+ 1 derivative is equal to (n+ 1)!