Logarithmic Differentiation for (1+x)^(1/x): Finding dy/dx

[chapsticks]

Homework Statement

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

Homework Equations

dy/dx

The Attempt at a Solution

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)

 

[Mark44]

Homework Statement

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

Homework Equations

dy/dx

The Attempt at a Solution

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)

Do you have a question?

 

[chapsticks]

Yes, I want to check my work if it's correct.