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What's difference between (∂y/∂x) and (dy/dx)

  1. Mar 27, 2009 #1
    Hi all.
    Can anyone tell me what's difference between (∂y/∂x) and (dy/dx) and (fx) and (y`)?

    Thanks.(please tell me my probable English mistakes!)

    I asked this a few month ago but it seems that images in topic are not avaible (I think I have removed it from my server )
  2. jcsd
  3. Mar 27, 2009 #2
    ∂y/∂x and fx are http://en.wikipedia.org/wiki/Partial_derivative" [Broken]. They are applied to functions of several real variables, for example f(x,y)=x2+y2.

    dy/dx or y' is the ordinary derivative of a function of a single real variable such as y(x)=1/x.
    Last edited by a moderator: May 4, 2017
  4. Mar 27, 2009 #3
    Thank you.
    and another question:
    I have read this in my book =>

    My question is : although V function has more than one variable why the author has used (dv/dx) instead of ∂v/∂x?(y and x are variables)
    (you said that dy/dx is used when there is a single variable).
  5. Mar 27, 2009 #4


    Staff: Mentor

    v = y/x is a commonly used substitution for solving differential equations that involve y and x. It is assumed that y is a function of x. Although v is in terms of y and x in the substitution, v is ultimately a function of x, so it's reasonable to write its derivative as dv/dx

    In functions of two or more variables, as yyat mentioned, it is not assumed that any one independent variable is related to any other independent variable.
  6. Mar 28, 2009 #5
    Thank you all.
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