y=[x/(1+x)]^x
lny=x*ln(x/(1+x))
lny=lnx-ln(1+x)
两边求导,得：
y'/y=1/x-1/(x+1)
y'=y*(1/x-1/(x+1))
y'=y/(x(x+1))
y'=1/(x(x+1))*[x/(1+x)]^x