取对数,lny=x^xln(x)
令z=x^x,lnz=xln(x)
z'/z=ln(x)+1
z'=z[ln(x)+1]=(x^x)·[ln(x)+1]
y=(x^x)^x
lny=x^xln(x)
y'/y=(x^x)'·ln(x)+x^x·ln'(x)=(x^x)·[ln²(x)+ln(x)]+x^(x-1)
y'=[(x^x)^x]·{(x^x)·[ln²(x)+ln(x)]+x^(x-1)}