Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Notation Question

  1. May 27, 2010 #1
    Hi All,

    I have a question about notation.

    Suppose I have an expression:


    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)?

  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]?

    Last edited: May 28, 2010
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Notation Question
  1. Notation Question (Replies: 1)

  2. A question of notation (Replies: 1)