Deriving the Equation for Relativistic Mass

[digital19]

Homework Statement

Show that [tex]d(\gamma mu)=m(1- \frac{u^2}{c^2})^{-3/2} du[/tex]

Homework Equations

It is known that is
[tex]\gamma=\frac{1}{\sqrt{{1- \frac{u^2}{c^2}}}}[/tex]

The Attempt at a Solution

The question stated in part 1 is the precise question given in the textbook.

I'm not sure how to proceed here. I believe it's asking you to take the derivative using the product rule. I even wondered if it was a type and du was supposed to be on the left hand side.

 

[CompuChip]

It's not a typo,
[tex]d(\gamma mu)=m(1- \frac{u^2}{c^2})^{-3/2} du[/tex]
is just physicists' notation for
[tex]\frac{d}{du} (\gamma mu)=m(1- \frac{u^2}{c^2})^{-3/2} [/tex]
(if you want, consider du as an infinitesimal quantity, dividing by it gives you a differential quotient aka derivative on the left hand side).
So indeed, you just plug in the expression for [itex]\gamma[/itex] you gave and differentiate w.r.t. u; then simplify to get the requested result

 

[pam]

What text are you using?
[tex]u^2[/tex] stands for [tex]\vec u}\cdot{\vec u}[/tex].
This leads to an additional term in the derivative.