Force using relativistic momentum

[jk4]

[SOLVED] Force using relativistic momentum

I have an example problem in a textbook I'm reading:

"Find the acceleration of a particle of mass m and velocity v when it is acted upon by the constant force F, where F is parallel to v.

then it proceeds to show the solution:

$$F = \frac{d}{dt}(\gamma mv) = m\frac{d}{dt}(\frac{v}{\sqrt{1-v^{2}/c^{2}}})$$

I get all that so far. The next step is where it loses me:

$$= m[\frac{1}{\sqrt{1-v^{2}/c^{2}}} + \frac{v^{2}/c^{2}}{(1-v^{2}/c^{2})^{3/2}}] \frac{dv}{dt}$$

so I don't know how they got there... and then the next step confuses me also. They go from above to here:

$$= \frac{ma}{(1-v^{2}/c^{2})^{3/2}}$$

and then of course there a few more steps after that one, but I can get those, I'm just confused about those two steps. Please help clarify it for me, thank you.

 

[Doc Al]

The first step: Use the product (or quotient) rule for taking a derivative.
The second step: Simplify. Start by getting a common denominator.

 

[jk4]

ah, of course. I see it now. Thank you for the quick reply.

 

[sharara92]

I still can't Simplify it to the final form .. can anybody help me with that?? Thank you