Results 1 to 6 of 6

Math Help - Find f_(xy)

  1. #1
    Junior Member
    Joined
    Nov 2009
    Posts
    38

    Find f_(xy)

    Find f_{(xy)} for f(x,y)=\frac{4x^2}{y}+\frac{y^2}{2x}

    I did one with f_{x}(x,y)\ for\ f(x,y)=e^{xy}(cos x\ sin x)

    and got e^{xy}(sin x\ siny)

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Dec 2008
    From
    Scotland
    Posts
    901
    Quote Originally Posted by JJ007 View Post
    Find f_{(xy)} for f(x,y)=\frac{4x^2}{y}+\frac{y^2}{2x}

    I did one with f_{x}(x,y)\ for\ f(x,y)=e^{xy}(cos x\ sin x)

    and got e^{xy}(sin x\ siny)

    Thanks
    Differentiate once w.r.t x, keeping everything else as constant. Then differentiate the results w.r.t y, keeping everything else as constant.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    28
    f=\frac{4x^2}{y}+\frac{y^2}{2x}

    f=4x^2y^{-1}+\frac{y^2x^{-1}}{2}

    Take derivative w.r.t x of f

    f_x=8xy^{-1}+\frac{-y^2x^{-2}}{2}

    f_x=8xy^{-1}+\frac{-y^2x^{-2}}{2}

    Take derivative w.r.t y of f_x

    f_{xy}=-8xy^{-2}+\frac{-2yx^{-2}}{2}

    Anygood?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Dec 2008
    From
    Scotland
    Posts
    901
    Quote Originally Posted by pickslides View Post
    f=\frac{4x^2}{y}+\frac{y^2}{2x}

    f=4x^2y^{-1}+\frac{y^2x^{-1}}{2}

    Take derivative w.r.t x of f

    f_x=8xy^{-1}+\frac{-y^2x^{-2}}{2}

    f_x=8xy^{-1}+\frac{-y^2x^{-2}}{2}

    Take derivative w.r.t y of f_x

    f_{xy}=-8xy^{-2}+\frac{-2yx^{-2}}{2}

    Anygood?
    Perfect.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Nov 2009
    Posts
    38
    Quote Originally Posted by Mush View Post
    Differentiate once w.r.t x, keeping everything else as constant. Then differentiate the results w.r.t y, keeping everything else as constant.
    Ok got it. So if I wanted f_{xx}(x,y) then I differentiate w.r.t.x twice right?
    f(x,y)=e^{x^2y}
    f_{x}(x,y)= 2xye^{x^2y}
    f_{xx}(x,y)=(4x^2+2y)e^{x^2y}
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member
    Joined
    Dec 2008
    From
    Scotland
    Posts
    901
    Quote Originally Posted by JJ007 View Post
    Ok got it. So if I wanted f_{xx}(x,y) then I differentiate w.r.t.x twice right?
    f(x,y)=e^{x^2y}
    f_{x}(x,y)= 2xye^{x^2y}
    f_{xx}(x,y)=(4x^2+2y)e^{x^2y}
    That's right.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 8
    Last Post: March 22nd 2011, 04:57 PM
  2. Replies: 2
    Last Post: July 5th 2010, 08:48 PM
  3. Replies: 1
    Last Post: February 17th 2010, 03:58 PM
  4. Replies: 0
    Last Post: June 16th 2009, 12:43 PM
  5. Replies: 2
    Last Post: April 6th 2009, 08:57 PM

Search Tags


/mathhelpforum @mathhelpforum