Question

y=x的x的x次方 用对数求导法求此函数的导数

Answer 1

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)]