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

  • #1
Ondina
3
0
<<Moderator note: Remember that filling in the complete homework template is mandatory in the homework forums. This thread has not been deleted due to containing relevant replies.>>

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

 
Last edited by a moderator:

Answers and Replies

  • #2
BvU
Science Advisor
Homework Helper
15,268
4,244
Hello Ondina, welcome to PF :smile: !

<<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: $$\left (e^{\ln x\over x} \right )'= e^{\ln x\over x} \; \left ({\ln x\over x} \right )'
$$.
 
Last edited by a moderator:
  • #3
22,330
5,205
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
 
  • #4
Ondina
3
0
Thank you all very much for your help!
 

Suggested for: Complex derivative of x: ((x)^(1/x))'

Replies
29
Views
813
Replies
6
Views
227
Replies
24
Views
617
Replies
32
Views
832
Replies
3
Views
447
Replies
1
Views
788
Replies
2
Views
324
  • Last Post
Replies
3
Views
409
Top