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Notation Question

  1. May 27, 2010 #1
    Hi All,

    I have a question about notation.

    Suppose I have an expression:

    [tex]f(x,g(x,y))[/tex]

    I would like to know how to express (not calculate) the rate of change of the above expression with regards to x.

    I can always express it like this:

    Let [tex]z(x,y) = f(x,g(x,y))[/tex]. Rate of change is [tex]\frac{{\partial z}}{{\partial x}}[/tex].

    But that is awkward. Is there any way to express [tex]\frac{{\partial z}}{{\partial x}}[/tex] without having to introduce a variable z (i.e. using only variables and function names f,g,x,y)?

    Thanks,
    GZ
     
  2. jcsd
  3. May 27, 2010 #2
    what's wrong with partial f/ partial x ?

    ahh i see

    what you want is

    [tex] \frac{\partial f\big|_{y=g}}{\partial x}[/tex]

    or if you feel there might be ambiguity about whether the derivative is evaluated at g or f

    [tex] \frac{\partial (f\big|_{y=g})}{\partial x}[/tex]

    honestly though

    [tex] \frac{\partial }{\partial x} f(x,g)[/tex] is probably best
     
    Last edited: May 27, 2010
  4. May 27, 2010 #3
    Hi ice109,

    Thank you for your response.

    What I really want is the quantity [tex]\frac{\partial z}{\partial x}=\frac{\partial f}{\partial x}+\frac{\partial f}{\partial g}\frac{\partial g}{\partial x}[/tex].

    [tex]\frac{\partial f}{\partial x}[/tex] does not reflect the second term above.

    But do I have to introduce a new variable z in order to express this clearly? Or is there a better way?


    I have never see the notation [tex]\frac{\partial}{\partial x} f(x,g)[/tex] before. Does it equal [tex]\frac{{\partial f}}{{\partial x}} +\frac{\partial f}{\partial g}\frac{\partial g}{\partial x}[/tex]?

    Thanks,
    gz
     
    Last edited: May 28, 2010
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