Question

How do you find the derivative of `(1+x)^(1/x)`?

Answer 1

`(1+x)^(1/x) [-1/x^2 ln(1+x) + 1/(x(1+x))]`

Let y= `(1+x)^(1/x)`
ln y= `1/x ln(1+x)`. Now differentiate,

`1/y dy/dx= (-1/x^2) ln(1+x) + 1/x * 1/(1+x)`

`dy/dx = (1+x)^(1/x) [-1/x^2 ln(1+x) + 1/(x(1+x))]`