Results 1 to 3 of 3

Math Help - Derivative of this exponential function?

  1. #1
    Junior Member
    Joined
    Nov 2009
    From
    US
    Posts
    27

    Derivative of this exponential function?

    what is the derivative of x^(e^x)?

    Is it [e^x][x^(e^x - 1)]?

    Or is there something else that I have to do. thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor harish21's Avatar
    Joined
    Feb 2010
    From
    Dirty South
    Posts
    1,036
    Thanks
    10
    Quote Originally Posted by mneox View Post
    what is the derivative of x^(e^x)?

    Is it [e^x][x^(e^x - 1)]?

    Or is there something else that I have to do. thanks!
    Follow this link and click on "Show steps":

    differentiate x^(e^x) - Wolfram|Alpha
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by mneox View Post
    what is the derivative of x^(e^x)?

    Is it [e^x][x^(e^x - 1)]?

    Or is there something else that I have to do. thanks!

    Write f(x):=x^{e^x}=e^{e^x\ln x}\Longrightarrow f'(x)=e^{e^x\ln x}\left[e^x\ln x+\frac{e^x}{x}\right] =x^{e^x}\left[e^x\ln x+\frac{e^x}{x}\right] =x^{e^x}\ln\left(x^{e^x}\right)+e^xx^{e^x-1} .

    Tonio
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. derivative of exponential function
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 23rd 2010, 10:30 AM
  2. Derivative of exponential function
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 27th 2010, 05:00 AM
  3. First derivative of exponential function
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 31st 2008, 01:24 PM
  4. Exponential Function Derivative
    Posted in the Calculus Forum
    Replies: 2
    Last Post: August 30th 2008, 03:38 PM
  5. Derivative of exponential function
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 10th 2007, 03:31 AM

Search Tags


/mathhelpforum @mathhelpforum