Question

f(x) = (lnx) / (x + 1) 
f ' (e) 

Answer 1

$f(x)=frac{lnx}{x+1}\\f`(x)=frac{frac{1}{x}(x+1)-lnx}{(x+1)^2}=frac{x+1-xcdot lnx}{x(x+1)^2}=frac{x(1-lnx)+1}{x(x+1)^2}\f`(e)=frac{e(1-lne)+1}{e(e+1)^2}=frac{1}{e(x+1)^2}; ; ; ; [lne=1; to ; (1-lne)=0]$