Question

x的x次方,怎么求导

Answer 1

y=x^x

=e^[ln(x^x)]

=e^(xlnx)

令u=xlnx,则y=e^u

y'=(x^u)'•u'

=(e^u)•(xlnx)'

=[e^(xlnx)]•[x'lnx+x(lnx)']

=[e^(xlnx)]•(lnx+x•1/x)

=(x^x)(1+lnx)