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Deriving with multiple variables

  1. Sep 2, 2013 #1
    1. The problem statement, all variables and given/known data
    I'm stuck at one of the derivations for relativistic energy. I've figured out every other single step, but I just can't wrap my head around this one:

    Prove that:

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


    2. Relevant equations
    u is speed, so:

    [tex] u = dx/dt [/tex]
    I don't know if that's helpful.


    3. The attempt at a solution
    I've tried everything that's in my calculus toolbox, but I guess that's not a whole lot. I know how to derive basic functions, but I just can't seem to figure out how turn this into something I can work with. It says to derive to t, but there's not even a t in the function. I know that u and t are related in a way, but substituting just leads to more trouble.
     
  2. jcsd
  3. Sep 2, 2013 #2
    Speed depends on time, u = u(t), so you just need to use the chain rule:[tex] \frac{d f(u(t))}{dt} = \frac{df}{du} \frac{du}{dt} [/tex]
     
  4. Sep 2, 2013 #3
    Alright, I've got it now. Thanks!
     
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