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Quick Question

  1. Jan 30, 2008 #1
    Say I have a function [tex]g = g(x,y)[/tex]. Now, I have another function defined as:
    [tex]f(x,y) = \partial / \partial x [g(x,y)][/tex]. Is the following true:

    [tex]f(a,b) = (\partial / \partial x [g(x,y)])_{x = a, y = b} = \partial / \partial a [g(a,b)][/tex]

    a, b, x, y are all variables. Is this true in general for any function of any number of variables?
     
  2. jcsd
  3. Jan 30, 2008 #2
    It looks like you just substituted a for x and b for y. So I guess the answer is yes, you can do that :).
     
  4. Jan 30, 2008 #3
    To me that looks like the partial derivative of g with respect to x, at the point (a,b). It's better without that middle part, if you just want to give the variables a different set of 'labels'.
     
  5. Jan 30, 2008 #4
    Yes, you're right in your interpretation. However, the equality between the middle part and the last part is the most crucial step for my purposes, so I can't take it out.
     
  6. Jan 31, 2008 #5

    HallsofIvy

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    The only difference between the "middle" and "last" parts of you statement are that in the middle part, you differentiate using the "symbols" x and y, then replace them by a and b, while, in the last part, you replace x and y by a and b, then differentiate. Yes, those are equal.
     
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