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Taylor expansion of x^x

  1. Sep 17, 2010 #1
    hello,
    please help to calculate the taylor polynomial for
    [URL]http://latex.codecogs.com/gif.latex?f(x)=x^{x}-1[/URL] around the point a=1

    i thought to write it as g(x)=x^x
    and then f(x)=g(x)-1
    and then find the polynomial for g(x) as lng(x)=xln(x)
    but it seems incorrect.
     
    Last edited by a moderator: Apr 25, 2017
  2. jcsd
  3. Sep 17, 2010 #2

    hunt_mat

    User Avatar
    Homework Helper

    In order to do this you have to calculate the derivative if [tex]y=x^{x}$[/tex], take logs of this equation and differentiate that using implicit differentiation and that will help you, or you could write:
    [tex]
    x^{x}=e^{x\log x}
    [/tex]
    And use the chain rule
     
  4. Sep 17, 2010 #3
    thanks,
    successfully managed by directly calculating the taylor polynomial when
    [URL]http://latex.codecogs.com/gif.latex?f(x)=e^{xlnx}[/URL]
     
    Last edited by a moderator: Apr 25, 2017
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