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"

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- Feb 4th 2010, 08:40 AMroshanheroDifferentiation
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" - Feb 4th 2010, 11:45 AMAryth
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.