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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.

K V
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1 Answers1

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Ok I think I find FaĆ  di Bruno's formula : https://en.wikipedia.org/wiki/Fa%C3%A0_di_Bruno%27s_formula

K V
  • 33