Pith Derivative

Problem inspired by Derintegrals .

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$\frac{d^{\alpha}}{dx^{\alpha}}x^{k}= \frac{\Gamma (k+1)}{\Gamma (k+1-\alpha)}x^{k-\alpha}$

$\left [ \frac{d^{\pi}}{dx^{\pi}}_{|x=\phi}(x^{e}) \right ]$

$=\left [ \frac{\Gamma (e+1)}{\Gamma (e+1-\pi)}x^{e-\pi} _{|x=\phi} \right ]$

$=\left [ \frac{e!}{(e-\pi)!}\phi^{e-\pi} \right ]$ ( $\leftarrow$ clickable)

$=\left [ 2.249... \right ]$

$=\boxed{2}$

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See Fractional Calculus .

Thanks to Michael Mendrin for making me aware of this.

u made my day...thank you for making me aware of this

Okay, you win for probably the most weird problem posted here on Brilliant that I've seen. But, the notation for the Floor function, aka greatest integer function, is $\left\lfloor weird\quad expression\quad here \right\rfloor$ . The brackets you're using here is an older form for it, and should be reserved only for nearest integer function, aka round.

I hadn't encountered a fractional derivative before.

Using equation (6) in the link, I plugged in the appropriate values and came up with an answer of $\lfloor 2.2492635.... \rfloor = \boxed{2}$ .