Hi,

For the first part of your question, a geberal formula can be reached in Gamma function as follows:

restart;

y := x -> x^n;

convert(combine(diff(y(x),x$m)),GAMMA);

or in terms of factorial function it can be written as:

convert(convert(diff(y(x),x$m),GAMMA), factorial);

The second part of your question is obscure for me.

Good luck.

I attach a maple file.

Hope it solves your problem.
 

Download a_solution.mw

Hello,

I saw your file. In such cases, you first must use "with(Physics)" (which you have also used in your file).

Then, it is sufficient to use the following code instead of your last code for your end:

>diff(L, diff(t(lambda), lambda))

I checked and got the correct answer (-(-r+2*m)*(diff(t(lambda), lambda))*(1/r)).

Good luck.