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

1. Mar 27, 2009

Hamid1

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. Mar 27, 2009

yyat

∂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
3. Mar 27, 2009

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).

4. Mar 27, 2009

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.

5. Mar 28, 2009

Hamid1

Thank you all.