51问答网 > 同济高数上册：幂函数导数使用导数定义推导的疑问？？？

同济高数上册：幂函数导数使用导数定义推导的疑问？？？

(X^n-A^n)/(X-A)==? 怎么求解这个计算呢？O(∩_∩)O谢谢。。。。。
2025-03-15 00:01:45
推荐回答（1个）
回答1：

解：X^n-A^n=A^n((X/A)^n-1)=A^n(X/A-1)((X/A)^(n-1)+(X/A)^(n-2)+……+X/A+1)
=(X-A)(X^(n-1)+AX^(n-2)+A^2*X^(n-3)+……+A^(n-2)*X+A^(n-1))
∴(X^n-A^n)/(X-A)=X^(n-1)+AX^(n-2)+A^2*X^(n-3)+……+A^(n-2)*X+A^(n-1)

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