d/dx e^x

This is a discussion on d/dx e^x within the A Brief History of Cprogramming.com forums, part of the Community Boards category; Why does d/dx e^x = e^x instead of xe^(x-1)...

  1. #1
    l'Anziano DavidP's Avatar
    Join Date
    Aug 2001
    Location
    Plano, Texas, United States
    Posts
    2,738

    Question d/dx e^x

    Why does

    d/dx e^x = e^x

    instead of

    xe^(x-1)
    My Website

    "Circular logic is good because it is."

  2. #2
    Pursuing knowledge confuted's Avatar
    Join Date
    Jun 2002
    Posts
    1,916
    Because you can't use the power rule with functions raised to a variable.

    d/dx k^x = k^(bx)*ln k*b
    Away.

  3. #3
    l'Anziano DavidP's Avatar
    Join Date
    Aug 2001
    Location
    Plano, Texas, United States
    Posts
    2,738
    you mean constants raised to a variable?
    My Website

    "Circular logic is good because it is."

  4. #4
    Mayor of Awesometown Govtcheez's Avatar
    Join Date
    Aug 2001
    Location
    MI
    Posts
    8,825
    Originally posted by DavidP
    you mean constants raised to a variable?
    Either one.

    Instead of using a shortcut rule, actually put it through the long definition of a derivative and work it out.

  5. #5
    Registered User whistlenm1's Avatar
    Join Date
    Jan 2002
    Posts
    124
    for me I did not understand it until I found a proof, so unless your going to look at a proof take it as is.
    Man's mind once streched by a new idea, never regains its original dimensions
    - Oliver Wendell Holmes

    In other words, if you teach your cat to bark (output) and eat dog food (input) that doesn't make him a dog. It would have to chase cars, chew bones, and have puppies before I'd call it Rover ;-)
    - WaltP

  6. #6
    Registered User
    Join Date
    Nov 2002
    Posts
    1,109
    just take it as it is. but if you want to know why, as cheez said, put it through the long definition of the derivative.

  7. #7
    Pursuing knowledge confuted's Avatar
    Join Date
    Jun 2002
    Posts
    1,916
    http://archives.math.utk.edu/visual....definition.12/ The definition of a derivative can be found there if you want to have a go at it
    Away.

  8. #8
    Banned
    Join Date
    Jan 2003
    Posts
    1,708
    so is this setup what cheez and you guys meant:


    (e^(x+h) - e^(x)) / (h)
    Lim h->0

    I saw what confuted put for the answer but I'm not 100% sure the steps you have to take to get there.

    EDIT: does b stand for base above? (change of base)
    Last edited by Silvercord; 11-03-2003 at 03:38 PM.

  9. #9
    Pursuing knowledge confuted's Avatar
    Join Date
    Jun 2002
    Posts
    1,916
    b and k were arbitrary constants.

    (e^(x+h) - e^(x)) / (h)
    Lim h->0

    (e^((x+h)/x)) / (h)
    Lim h->0

    You'll have to take an ln() in there to get that to something you can work with.
    Away.

  10. #10
    Toaster Zach L.'s Avatar
    Join Date
    Aug 2001
    Posts
    2,686
    Use the Maclaurin series for e^x, and it becomes really obvious:

    e^x = sum(k=0, infinity) [ x^k / k! ]

    So for each term,
    d[x^k / k!]/dx = k*x^(k-1) / k! = x^(k-1) / (k-1)

    That is, when you take the derivative, each term becomes its predecessor, so the series remains unchanged.
    The word rap as it applies to music is the result of a peculiar phonological rule which has stripped the word of its initial voiceless velar stop.

Popular pages Recent additions subscribe to a feed

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21