Question

How do you differentiate `(1+x)^(1/x)`?

Answer 1

`y'=(1/(x(1+x))-1/x^2 ln(1+x))(1+x)^(1/x)`

Explanation:

`y=(1+x)^(1/x)`

`lny=ln((1+x)^(1/x))`

`lny=1/xln(1+x)`

`d/dx(lny)=d/dx(1/xln(1+x))`

`1/yy'=-1/x^2 ln(1+x)+1/x 1/(1+x)`

`y'=(1/(x(1+x))-1/x^2 ln(1+x))(1+x)^(1/x)`