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

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May 13, 2015

# (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))]#

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