This doesn't seem to be working? Relativity

[IntegrateMe]

Evaluate the derivative of $$\vec{F} = \frac {d} {dt} \frac {m \vec{v}} {\sqrt{1 - v^2/c^2}}$$ to find the acceleration $$a = \frac {dv}{dt}$$ of the particle.

So, basically, I just tried to use the quotient rule and treat m, and the whole bottom of the fraction as constants. I didn't end up getting the right answer and I can't figure out why. As reference, here are two answers I've tried, both wrong:

$$\frac {F}{m} \sqrt {1 - \frac {v^2}{c^2}}$$
$$\frac {F}{m} (1 + \frac {v^2}{3c^2})$$

 

[SammyS]

Evaluate the derivative of $$\vec{F} = \frac {d} {dt} \frac {m \vec{v}} {\sqrt{1 - v^2/c^2}}$$ to find the acceleration $$a = \frac {dv}{dt}$$ of the particle.

So, basically, I just tried to use the quotient rule and treat m, and the whole bottom of the fraction as constants. I didn't end up getting the right answer and I can't figure out why. As reference, here are two answers I've tried, both wrong:

$$\frac {F}{m} \sqrt {1 - \frac {v^2}{c^2}}$$
$$\frac {F}{m} (1 + \frac {v^2}{3c^2})$$

How can you treat v² as a constant?

 

[elfmotat]

Remember the fact that:

$$\frac{dv}{dt}=\frac{\vec{a}\cdot \vec{v}}{v}$$