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

[Hamid1]

Hi all.
Can anyone tell me what's difference between (∂y/∂x) and (dy/dx) and (f_x) 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 )

 

[yyat]

∂y/∂x and f_x are http://en.wikipedia.org/wiki/Partial_derivative" . 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.

 

[Hamid1]

Thank you.
and another question:
I have read this in my book =>
v=y/x
dv/dx=...

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).

 

[Mark44]

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 anyone independent variable is related to any other independent variable.

 

[Hamid1]

Thank you all.