calculus
posted by CyrusDelaney .
Use logarithmic differentiation to find dy/dx for y=(1+x)^(1/x).

ln y = ln (1+x)^(1/x)
= (1/x) ln (1+x)
(dy/dx) /y = (1/x^2)(ln(1+x) + (1/x)(1/(1+x)
dy/dx = y [(1/x^2) ( ln(1+x) + x/(1+x) ]
or (1/x^2)( ln(1+x) + x/(1+x) ) (1+x)^(1/x)
pretty messy looking ...