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有关幂指式xy 的数学问题 ,由于针对性解题工具的匮乏 ,解题难度往往较大 .而函数f(x) =lnxx 则可担起重任 ,是不可多得的解决此类问题的利器 .先用极限和导数研究函数 f(x) =lnxx的性质和图像 .∵ f′(x) =1 -lnxx2 知x ∈ ( 0 ,e)时 ,f′(x) 0 ;x∈ (e,+∞ )时 ,f′(x) 0
With respect to the mathematical problem of the exponent xy, due to the lack of targeted problem-solving tools, the difficulty of solving the problem is often greater, and the function f(x) = lnxx can take up heavy responsibilities and is a rare weapon to solve such problems. First study the properties and the image of the function f(x) = lnxx with the limit and the derivative. ∵ f′(x) =1 -lnxx2 When x ∈ (0, e) is known, f′(x) 0 ; x∈ (e , +∞ ), f’(x) 0