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

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Answer 1 · 2015-05-13T17:16:32

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

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

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

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

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