Results 1 to 4 of 4

Math Help - Differentiate ln(1+e^x) from first principles.

  1. #1
    Newbie
    Joined
    Nov 2010
    Posts
    1

    Differentiate ln(1+e^x) from first principles.

    Hi,

    First post here

    Anyway, I'm currently stuck on this question and I have no idea how to get any furfther, so I would really appreciate any help with it.

    Differentiate using first principles:

    f(x) = ln(1+e^x)

    I've managed to get to this point:

    f'(x) = lim(h -> 0) (ln((e^x+e^-h)/(e(^x)+1)))/h

    But I don't know how to get rid of the log, or the h's for that matter.


    Cheers, Paul.

    Edit: Sorry the thread title should say exponential functions, too tired.
    Last edited by Intrepid44; November 20th 2010 at 02:38 PM. Reason: Title
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Dec 2009
    From
    1111
    Posts
    872
    Thanks
    3
    Quote Originally Posted by Intrepid44 View Post
    Hi,

    First post here

    Anyway, I'm currently stuck on this question and I have no idea how to get any furfther, so I would really appreciate any help with it.

    Differentiate using first principles:

    f(x) = ln(1+e^x)

    I've managed to get to this point:

    f'(x) = lim(h -> 0) (ln((e^x+e^-h)/(e(^x)+1)))/h

    But I don't know how to get rid of the log, or the h's for that matter.


    Cheers, Paul.

    Edit: Sorry the thread title should say exponential functions, too tired.
    Dear Intrepid44,

    Please refer the attached pdf file. If you have any questions please do not hesitate to ask me.
    Attached Thumbnails Attached Thumbnails Differentiate ln(1+e^x) from first principles.-sp.pdf  
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    14,974
    Thanks
    1121
    Ah, Sudharaka used the Taylor's series expansion for e^x. That's clever!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Dec 2009
    From
    1111
    Posts
    872
    Thanks
    3
    Quote Originally Posted by HallsofIvy View Post
    Ah, Sudharaka used the Taylor's series expansion for e^x. That's clever!
    Thanks HallsofIvy. Subscribed to this thread a couple of days ago, and thought about this problem for some time, since this is something that I havent encountered before.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: June 6th 2011, 08:46 AM
  2. Replies: 3
    Last Post: May 12th 2011, 05:30 AM
  3. Is the first principles?
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 21st 2010, 03:41 AM
  4. Differentiate from first principles?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 5th 2008, 01:11 PM
  5. first principles
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 5th 2008, 06:37 PM

Search Tags


/mathhelpforum @mathhelpforum