Results 1 to 5 of 5

Math Help - 2nd Order Partial Derivitive

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    9

    2nd Order Partial Derivitive

    Hello.

    I have a real issue with fractions, it seems! can anyone help me understand how to find the 2nd order derivitives for
    z=xy/(x+y)

    thanks for any help
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,234
    Thanks
    27
    There are four to find. \frac{\partial ^2z}{\partial x^2}, \frac{\partial ^2z}{\partial y^2}, \frac{\partial ^2z}{\partial xy} and \frac{\partial ^2z}{\partial yx}

    You need to find \frac{\partial z}{\partial x} and \frac{\partial z}{\partial y} first, use the quotient rule.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2009
    Posts
    9
    Yeah sorry I know, and I know how to do partial derivitives, its just that I always get my numbers messed up when I have fractions, I'll try again, but for all I know I'm not even using the quotient rule correctly!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Oct 2009
    Posts
    9
    okay, so (xy)/(x+y).
    Use quotient rule
    (y).(x+y)-(xy).(y) / (x+y)^2... is that right??? now what?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,234
    Thanks
    27
    for y = \frac{u}{v} then y' = \frac{vu'-uv'}{v^2}

    I get

     \frac{\partial z}{\partial x} = \frac{(x+y)(xy)'-(xy)(x+y)'}{(x+y)^2}= \frac{(x+y)y-(xy)\times 1}{(x+y)^2}= \frac{y^2}{(x+y)^2}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Partial Order
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: November 28th 2011, 02:28 PM
  2. Partial Order
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 28th 2011, 12:02 PM
  3. Partial Derivitive Question
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 5th 2011, 03:23 AM
  4. Contour Maps, Partial-Derivitive Help
    Posted in the Calculus Forum
    Replies: 0
    Last Post: January 31st 2009, 01:46 PM
  5. Partial Derivitive help
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 28th 2007, 07:54 AM

Search Tags


/mathhelpforum @mathhelpforum