Results 1 to 4 of 4

Math Help - showing f'(-x)=f'(x)

  1. #1
    Newbie
    Joined
    Oct 2007
    Posts
    16

    Question showing f'(-x)=f'(x)

    Show that the derivative of an odd function is even. That is, if f(-x)=-f(x), then f'(-x)=f'(x). Without using a specific example.
    Last edited by unluckykc; October 25th 2007 at 10:58 PM. Reason: I forgot to tyoe a sentence.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,666
    Thanks
    1617
    Awards
    1
    f\left( { - x} \right) =  - f(x)
    D_x \left( {f\left( { - x} \right)} \right) = f'( - x)( - 1) =  - f'( - x)
    D_x \left( { - f\left( x \right)} \right) =  - f'(x)
    f'(x) = f'( - x)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2007
    Posts
    16
    I don't understand how you got the last line. How does f'(x)=f'(-x)?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,666
    Thanks
    1617
    Awards
    1
    \begin{array}{l}<br />
  - f'( - x) = D_x (f( - x)) = D_x ( - f(x)) =  - f'(x) \\ <br />
 f'( - x) = f'(x) \\ <br />
 \end{array}<br />
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Showing being even
    Posted in the Geometry Forum
    Replies: 2
    Last Post: September 7th 2011, 10:06 AM
  2. showing
    Posted in the Algebra Forum
    Replies: 4
    Last Post: June 18th 2011, 04:54 AM
  3. Showing that Z<x,y> is not a UFD
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: January 27th 2010, 09:37 AM
  4. showing
    Posted in the Calculus Forum
    Replies: 2
    Last Post: August 20th 2009, 12:17 PM
  5. Showing That it is onto?
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: October 9th 2008, 08:00 AM

Search Tags


/mathhelpforum @mathhelpforum