Well, there are two ways to do this. Firstly, you can substitute for , which is what you've done here:

And which we can simplify:f^(n+1).(x) = −[(2(n+1)!/4(n+1).(n+1)!.(2(n+1) − 1)].{(1 − x)^1/2−(n+1)}

To check our work, we can take the derivative of , like so:

And we can see that this does not check out. So, something is either wrong with my work or with the original functions. I believe it is the latter.

thanks in advance