There is the first derivative \(\dfrac{d}{dx}\)
and there is the second derivative \(\dfrac{d^2}{dx^2}f(x)=\dfrac{d}{dx}(\dfrac{d}{dx}(f(x)))\)
I wonder if there is something like a one third derivative?
Something like:
\(\dfrac{d^{1/3}}{dx^{1/3}}\)
\(\dfrac{d^{\sqrt2}}{dx^{\sqrt2}}\)
Or even:
\(\dfrac{d^{\pi}}{dx^{\pi}}\)
Or
\(\dfrac{d^{e}}{dx^{e}}\)
Even crazier:
\(\dfrac{d^{1+\sqrt3 i}}{dx^{1+\sqrt{3}i}}\)
I wonder if those things exists?