I find how to deal with limits (Nth Derivative of $y=f(x)$).
To deriviate without limits we have
$y'(x) = y'(f(x)) * f'(x) = \frac{\delta y}{\delta f} \frac{\delta f}{\delta x}$
$y''(x) = y''(f(x))f'(x)^2 + y'(f(x))f''(x)= \frac{\delta^2 y}{\delta^2 f}(\frac{\delta f}{\delta x})^2 + \frac{\delta y}{\delta x}\frac{\delta^2 f}{\delta^2 x}$
...
$y^{n} = ?$
I try to find a general form with maybe $\sum$'s and $\Pi$'s and maybe binomials. Maybe the name is General form of nth chain rule.