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Subscripts in partial derivative notation

  1. Mar 16, 2013 #1
    Hi everyone,

    We just started learning partial derivatives and I understand the fx notation, but I'm confused when I'm asked for the value of fxy. Does this mean multiply the two derivatives together?

    For example:

    What is fxy when f(x,y) = (x+2y)ln(xy)

    Thanks!
     
  2. jcsd
  3. Mar 16, 2013 #2

    micromass

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    It means [itex](f_x)_y[/itex]. So it asks for the partial derivative in the y-direction of ##f_x##.

    For example, if ##f(x,y)= x^2y+5y^2##, then ##f_x(x,y) = 2xy## and ##f_{xy}(x,y) = 2x##.
     
  4. Mar 16, 2013 #3
    So basically I'll take the partial derivative with respect to x, then take the derivative of that with respect to y?
     
  5. Mar 16, 2013 #4

    micromass

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    Yes.

    It is a curious property that (under very mild conditions), this is the same as taking the partial derivative with respect to y and then with respect to x. So ##f_{xy}=f_{yx}##.
     
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