Find the first derivative of y = x^(x - 2)

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/11 12:39:59

Find the first derivative of y = x^(x - 2)
找到y = x ^(x - 2)的一阶导数
y=x^(x-2)
两边取对数
lny=lnx^(x-2)
lny=(x-2)lnx
因为y是关于x的函数,两边对x求导
左边因为y是x的函数,根据复合函数求导,得y'/y
右边对x求导=(x-2)'*lnx+(x-2)*(lnx)',得lnx+(x-2)/x
y'/y=lnx+(x-2)/x
y'=y*[lnx+(x-2)/x]
因为y=x^(x-2),代入上式
得到y的导数
y'=x^（x-2）*[lnx+(x-2)/x]

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