About $\frac{\partial^n f}{\partial x^n}$ ,for $f(x)$,What should I think, when $n[\in (\mathbb R\backslash \mathbb Q)^+]$ or $(\in \mathbb C)$?

Question

About $\frac{\partial^n f}{\partial x^n}$ ,for $f(x)$,What should I think, when $n[\in (\mathbb R\backslash \mathbb Q)^+]$ ,pozitive irrational? or $(\in \mathbb C)$

For example;

$f(x)=x^2+3x\quad$ and $\quad n=\sqrt2\quad\to\quad \dfrac{\partial^{(\sqrt 2)} f}{\partial x^{(\sqrt2)}}=?$

and,

$f(x)=x^2+3x\quad$ and $\quad n=\sqrt i\quad\to\quad\dfrac{\partial^{(\sqrt i)} f}{\partial x^{(\sqrt i)}}=?$

And I think,I did grammar mistakes in the tittle, sorry about this.