0

As you can the question in the title, that is what I need to find $$\left(\frac{\,d}{\,dx}\right)^{\pi} x^{\mathrm{e}}$$ But I have never encountered anything in which we need to find the irrational derivatives, can anyone please help me.

Simply Beautiful Art
  • 74,685
Asv
  • 500
  • 1
    There are many different formalisms for derivatives like these, unfortunately they are not equivalent. They all rely on integrals, however. The two most popular are the one that use gamma function with the Cauchy integral, and the Fourier transform. Without any extra information there is no way of knowing which one is appropriate for your context. – Ninad Munshi Jun 20 '20 at 10:48
  • @NinadMunshi, so does that mean that it has no particular value? And can you also tell me those two ways you mentioned, I know that when the exponent of x and the derivative are equal, I can use the gamma function, but what can I do here? – Asv Jun 20 '20 at 10:53
  • 1
    See the wikipedia page on fractional calculus. It is hard for me to link since I'm on mobile. Both ideas are there (although the FT idea is explained using the Laplace transform instead, it is the exact same technique) – Ninad Munshi Jun 20 '20 at 10:54
  • @NinadMunshi, thanks I saw the page and according to that my answer should be $\frac{\mathrm{e}!}{\left(\mathrm{e}-\pi\right)!}x^{\mathrm{e}-\pi}$ – Asv Jun 20 '20 at 11:06

0 Answers0