> 0
>---
> 0
>
>is there such a mathematical symbol? ( 0 / 0 )

What do you mean by "is there"? And what do you mean by the word "symbol"?

You can of course write "0/0" and ponder its meaning. Would it symbolize anything? Yes, of course. It would symbolize a quandary people have been asking in droves. Does it symbolize any definite quantity - finite or infinite? Usually it does not. Not in the context of Calculus. But in some engineering problems I heard it is convenient to assign to 0/0 the value of 1.

>(0 / 0) / dx = 1 / x ?

Have no idea what you mean here. What is dx?

>dx / (0 / 0) = x ?
>
>can we have ddx ?

Depends on what yo mean by dx.