Proving using rodrigue's formula (a very challenging question)

[artisticmath]

This is a very challenging question I would like your help guys to solve this question.
Prove (n+1)Pn+1(x)-(2n+1)xPn(x)+nPn-1(x)=0 using Rodriguez's formula

 

[adjacent]

What have you tried so far?

 

[artisticmath]

The problem is in differentiating ..I really find it very difficult to differentiate..

 

[HallsofIvy]

You still haven't said what you tried. Or are you saying that, because you are "find it very difficult to differentiate", you simply haven't tried at all?

 

[artisticmath]

I am making a progress .. I found a formula that allowed me to differentiate (n+1) times, so now am working on finding Pn+1 and Pn-1 by the Rodriguez formula , and then substituting them back in the equation..