I am trying to prove that the group velocity is equal to the particle velocity by relativistic purpose
The relativistic energy is given by the relation
But I don't know how to differentiate it with respect to momentum "p"
Well, first you get E by itself:
Now, we take the derivative with respect to on both sides:
First we use the chain rule setting
Now, you differentiate what is in the parentheses:
The two's cancel, and a c factors out of the radical in the denominator, which simplifies the derivative to:
And that's the derivative, maybe you can continue with this.