# Complex derivative of x: ((x)^(1/x))'

Ondina
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1. Homework Statement

((x)^(1/x))'

## Homework Equations

This probably isn't overly dificult, but it has got me stumped, if anyone would be so kind as to reply, would you please post the entire process, so that I can try to better understand it. Thank you very much

## The Attempt at a Solution

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Homework Helper
Hello Ondina, welcome to PF !

<<Moderator note: Removed comment on now deleted full solution.>>

That way you are robbed from a learning experience that might have helped you in a future exercise.

If you see something like ##x^{1\over x}## it's sometimes helpful to write it as ##e^{\ln x\over x}##. To take the derivative you use the chain rule: $$\left (e^{\ln x\over x} \right )'= e^{\ln x\over x} \; \left ({\ln x\over x} \right )'$$.

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Mentor
BvU is making use of the relationship that:

##y = e^{\ln y}##

This follows from the definition of the natural log of a quantity: lny is the power you have to raise e to in order to get y.

Chet

Ondina
Thank you all very much for your help!