I am not sure what is supposed to be here, but something is an improvement on nothing, perhaps.

so here are some criticisms:

1. playground does not allow one to play.
2. I would not suggest \(\vec a\) as the name of an arbitrary vector, and certainly not \(\vec a_x\). But \(\hat e_x\) should be mentioned.
3. “While these points of view are equivalent,” if we agree on the directions of the coordinate system
4. “we never use subscripts to denote derivatives” Does anyone? Is this worth mentioning? I know in GR one uses subscripts preceeded by a comma or semicolon, but not without, I think. And in any case that seems premature to mentions here.

 Joel Shapiro

Responses by TD:

1. playground is locked down for security reasons;
2. have changed $\vec a$ to $\vec w$, but $\vec a_x$ is used in engineering to denote $x$ basis vector;
3. OK;
4. Yes! All calculus texts use subscripts to denote partial derivatives!