> 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.
i was fiddling around with implicit differentiation the other day.d (x^n) can be rewritten as
n / b * x ^ (n-b) * d(x^b),
where b is constant
so if b = 1, n = 2
d (x^2)
= x ^ (2-1) * d(2*x^1/1)
= x * d(2x)
= 2x * d(x)
but, what if b = 0
the RHS expression then becomes
n/0 * x^n d(x^0)
then d(x^0) = 0, since x^0 is a constant 1
i.e
d(x^n) = n*x^n * (0 / 0)
but
d(x^n) / dx = n*x^(n-1)
the RHS is n*x^n * (0/0)
i.e
n*x^n * (0/0) / dx = n*x^(n-1)
i.e
(0/0) / dx = 1 / x
dx / x = ? (0 / 0)?