1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Differentiate x^(x^2)

  1. Jun 8, 2009 #1
    1. The problem statement, all variables and given/known data
    Differentiate [tex]x^{x^2}[/tex], with respect to x

    2. Relevant equations

    [tex]\frac{d}{dx} (x^{x^2})[/tex]

    3. The attempt at a solution
    I arrived at... (ready?)

    (ta dah!): [tex]x^{x^2}.(2x.\ln(x)+x)[/tex]

    I'm pretty confident this is wrong...

    I went [tex]y(x)=x^{x^2}[/tex], then took the natural logarithm of both sides

    Since [tex]\ln(x^{x^2}) = x^2.\ln(x) and \frac{d}{d(y(x))} (ln (y(x))) = \frac{1}{y(x)}[/tex]

    I got:

    [tex]\frac{1}{y(x)} . \frac{d(y(x))}{dx} = \frac{d}{dx} (x^2.\ln(x))[/tex]

    [tex]\frac{1}{y(x)} . \frac{d(y(x))}{dx} = 2x.\ln(x)+\frac{x^2}{x}[/tex]

    [tex]\frac{d(y(x))}{dx} = 2x.\ln(x)+\frac{x^2}{x} . x^{x^2} = x^{x^2}.(2x.\ln(x)+x)[/tex]

    As I said, I think this is wrong. I've been working through examples all day and figured I might be able to come back to it, and hopefully figure it out (that is my excuse, and I'm sticking with it! :smile:); but since I don't have easy access to a computer, I thought I might ask you guys now, and check back tomorrow to see if anyone has offered any help.
    Thanks everyone.
  2. jcsd
  3. Jun 8, 2009 #2
    Eh I think that is right, though I did it in my head. It's easy if you write it as the exponential of (x^2)(ln x), from which you get the original expression times the derivative of (x^2)(ln x) which by the product rule is 2x(ln x) + x.
  4. Jun 8, 2009 #3


    User Avatar
    Homework Helper

    I don't see why you think this would be wrong, because it's not.
  5. Jun 8, 2009 #4
    Yup, I think it's pretty correct.
  6. Jun 9, 2009 #5
    Snipez90, Cyosis & Karkas: Thankyou.
    The question was from a multiple choice "quiz" that I saw, and I just didn't recognise the answer that I got (above) from being one of the possibilities: that's why I thought it was wrong. But it seems its not! Thanks for the responses everyone!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook