Question

y=x的x的x次方 用对数求导法求此函数的导数

要详细过程 具体些

Answer 1

取对数
lny=xlnx
对x求导
则(1/y)*y'=1*lnx+x*(1/x)=lnx+1
y=x^x
所以y'=x^x(lnx+1)

Answer 2

y=x^x
lny=xlnx
y'/y=lnx+1
y'=(x^x)(1+lnx)

z=x^(x^x)
lnz=(x^x)lnx
z'/z=lnx*[(x^x)(1+lnx)]+(x^x)*1/x
=[x^(x-1)]*[x(lnx)²+xlnx+1]
z'=[x(lnx)²+xlnx+1]*[x^(x^x+x-1)]

Answer 3

y = x^x = e^(lnx^x) = e^[xlnx]
y' = [e^(xlnx)][lnx + x/x]
= (x^x)(lnx + 1)

Answer 4

y = x^x = e^(lnx^x) = e^[xlnx]
y' = [e^(xlnx)][lnx + x/x]
= (x^x)(lnx + 1)