Results 1 to 6 of 6

Math Help - calculus stupidity....

  1. #1
    Newbie
    Joined
    May 2010
    Posts
    9

    calculus stupidity....

    I'm reading a problem in my book and they are going over the solution to a problem: If f(x) = 1/x, then f^4 (x) = 24/x^5.... How the heck did they get that? If I take the function to the 4th power, I get 1/(x^4)... Am I not mistaken?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Nov 2009
    Posts
    177
    If written as f^{(4)}(x), then it means the derivative of the 4th order (the parentheses are important).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor harish21's Avatar
    Joined
    Feb 2010
    From
    Dirty South
    Posts
    1,036
    Thanks
    10
    thats the 4th derivative of the function

    f(x)=1/x

    \frac{df(x)}{dx}= \frac{-1}{x^2}

    \frac{d^2f(x)}{dx^2}= \frac{2}{x^3}

    \frac{d^3f(x)}{dx^3}= \frac{-6}{x^4}

    \frac{d^4f(x)}{dx^4}= \frac{24}{x^5}
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    May 2010
    Posts
    9
    Ah, that would explain it, never seen it written that way, i always assumed f''''(x). Thanks.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    Joined
    Mar 2010
    Posts
    715
    Thanks
    2
    More generally, if \displaystyle f(x) = \frac{1}{x}, then:

    \displaystyle f^n(x) = \frac{(-1)^n\prod_{k=0}^{n-1}\left(n-k\right)}{x^{n+1}}.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by bobbooey View Post
    Ah, that would explain it, never seen it written that way, i always assumed f''''(x). Thanks.
    So what do you assume for the 37th derivative?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: December 13th 2011, 10:11 PM
  2. Replies: 1
    Last Post: February 11th 2010, 08:09 AM
  3. Calculus III But doesn't require Calculus :)
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 19th 2009, 05:23 PM
  4. Replies: 1
    Last Post: June 23rd 2008, 10:17 AM
  5. Replies: 1
    Last Post: June 7th 2008, 12:47 PM

Search Tags


/mathhelpforum @mathhelpforum