# Deriving with multiple variables

1. Sep 2, 2013

### Helices

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:

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

2. Relevant equations
u is speed, so:

$$u = dx/dt$$
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. Sep 2, 2013

### clamtrox

Speed depends on time, u = u(t), so you just need to use the chain rule:$$\frac{d f(u(t))}{dt} = \frac{df}{du} \frac{du}{dt}$$

3. Sep 2, 2013

### Helices

Alright, I've got it now. Thanks!