Is this derivative correct?

  • Thread starter dylanhouse
  • Start date
  • #1
42
0

Homework Statement



Find the derivative of y=x1/x

Homework Equations



Chain rule and logarithmic differentiation.

The Attempt at a Solution



y=x^(1/x)
lny=lnx^(1/x)
lny=(1/x)lnx
(1/y)y'=(1/x)lnx
y'=y((1/x)lnx)
y'=y((1/x)(1/x)+(lnx)(1/x))
y'=y((1/x^2)+(lnx/x))
y'=x^(1/x)((1/x^2)+(lnx/x))

Sorry for all the brackets, and if they are not correct :$
 

Answers and Replies

  • #2
In your 6th line I think I see a mistake you're using the product rule it seems? In the second part what did you take the derivative of?
 
  • #3
42
0
Should it read:

y'=y((1/x)(1/x)+lnx(1/x^2))?
 
  • #4
close shouldn't the derivative of x^-1 be -1*x^-2??
 
  • #5
42
0
So,
y'=y((1/x)(1/x)+lnx(-1/x^2))
y'=y((1/x^2)-(lnx/x^2))
y'=y(1-lnx/x^2)
 
  • #6
Looks good to me. Just plug in y like you did in the last step of the 1st post and you're golden.
 
  • #7
42
0
Thanks a bunch :)
 
  • #8
237
5
You have a problem with parentheses, but more importantly, lines 4 and 5 are very wrong.

You cannot differentiate the LHS and still equate it with the RHS without differentiating the RHS also.

However you still got there - as long as you correct your parentheses.
 
Last edited:

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