[BUG] multivariable chain rule

[Tevian Dray]

>> One problem with insisting  dp = (grad p) dot (d rvec) is that this
>> assumes there is an inner product present.

>> dp makes sense even if there is no inner product on the (u,v):
>> dp=p_u du+p_v dv.

Good point!  You are absolutely right, and in fact the gradient itself makes
no sense unless there is an inner product.  So let me rephrase my earlier
comments: The "Master Formula" (your first equation above) is good if you want
to talk about the gradient, including directional derivatives (and related
applications involving, say, velocities), but straight differentials (your
second equation) are best if you instead want to discuss the chain rule.

And I like your description in terms of "place-holders".  I sometimes talk
about differentials as "numerators of derivatives", a similar point of view.

Tevian