[VadeRetro]

Derive it? Newton's F = ma is strictly speaking wrong at any velocity, but produces observably wrong results at velocities near c. In particular, F = ma can be used to predict supraluminal velocities. (It assumes that if you keep pushing, you keep accelerating.) You're going to protest that it's the same formula and thus the same law under relativity, except that it requires the substitution

m = m₀ / (sqrt (1 - (v²/c²))

And I'm going to say that it's not really the same formula if it's not the same m.

[PatrickHenry]

I haven't posted a link to this in a long time: Why I No Longer Debate Idiots . If you haven't read it in a while, it's well worth the 2 minutes. This little essay contains much wisdom.

[AndrewC]

F = ma is strictly speaking wrong at any velocity, but produces observably wrong results at velocities near c. In particular, F = ma can be used to predict supraluminal velocities.

Acceleration and velocity are not the same thing.