Question

【X/(1+X)】的X次方怎么求导?

Answer 1

y=[x/(1+x)]^x

lny=x*ln[(x/(1+x)]

(lny)'= ln(x/(1+x))+x*(x/(1+x)'/[x/(1+x)]

y'/y=ln(x/(1+x))+(1-1/(1+x))' *(1+x)

=ln(x/(1+x0)+1/(1+x)

y'=[x/(1+x)]^x *[ln(x/(1+x))+1/(1+x)]