y=(1+1/x)^x (y等于1加x分之1的x次方)求导!

y=(1+1/x)^x,即y=e^ [x*ln(1+1/x)],所以y'= e^ [x*ln(1+1/x)] * [x*ln(1+1/x)] '而[x*ln(1+1/x)] '= x' * ln(1+1/x) + x* [ln(1+1/x)] '= ln(1+1/x) + x* [-(1/x^2) / (1+1/x)]= ln(1+1/x) - 1/(x+1)故y'= e^ [x*ln(1+1/x)] * [x*ln(1+1/x)] '= e^ [x*ln(1+1/x)] * [ln(1+1/x) - 1/(x+1)]= (1+1/x)^x * [ln(1+1/x) - 1/(x+1)]