# Differentiating Lorentz factor with respect to time

## Homework Statement

I would like some help on differentiating the lorentz factor with respect to time

## The Attempt at a Solution

i arrived at $$(-1/2) (1-v^2/c^2)^{-3/2}$$
but a forum on this website says it is $$(-1/2) (1-v^2/c^2)^{-3/2} ( \frac{-2v}{c^2} dv/dt)$$

cristo
Staff Emeritus
You want $$\frac{d}{dt}(1-v^2/c^2)^{-1/2}$$. Using the chain rule, this is equal to $$\frac{d}{dv}(1-v^2/c^2)^{-1/2}\frac{dv}{dt}=\left(\frac{-1}{2}\right)\left(\frac{-2v}{c^2}\right)(1-v^2/c^2)^{-3/2}\frac{dv}{dt}$$