1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Equal partial derivatives

  1. Nov 3, 2011 #1
    Hi, in general can we tell anything about the partial derivatives of a differentiable function if they are equal?

    for example I would like them to have to equal some constant. Would this be true?
     
  2. jcsd
  3. Nov 3, 2011 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Do you mean [itex]\partial f/\partial x= C[/itex] and [itex]\partial f/\partial y= C[/itex]? The same constant or different constants? From [itex]\partial f/\partial x= C[/itex], we get [itex]f(x,y)= Cx+ g(y)[/itex] where g can be any function of y. Differentiating that with respect to y, [itex]\partial f/\partial y= g'(y)= C[/itex] which tells us that g(y)= Cy+ C' where C' is an arbitrary constant of integration. That is, f(x,y)= Cx+ Cy+ C'.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Equal partial derivatives
  1. Partial derivative (Replies: 1)

  2. Partial derivative (Replies: 2)

  3. Partial derivatives (Replies: 1)

  4. Partial derivative (Replies: 21)

  5. The partial derivative (Replies: 2)

Loading...