Guy said:
Please don't follow "Guy Macon wrote" with something that I
clearly labeled (in the part you snipped) as being not my
question, but rather a question typical of a student in a
class I taught.
My apologies.
So you derive from deriving the derivative from the differential that
one should not differentiate between differential and derivative?
That's different.
Essentially yes. (Ignores irony). But then, I'm not only a
mathematician, I'm also a linguistics freak....
Google hits prove commonness of usage on the World Wide Web.
All else is derivative - an important difference.
<grin>
As I intimated, "common usage" is to be distrusted. After all, the
planet's population is now so large that virtually any human-behavioural
parameter, via the central limit theorem, gets modelled as obeying a
Gaussian distribution, whose *central* area dominates the sample results.
I call the universal welcome currently accorded to this situation "the
cult of mediocrity" and it is an example of positive feedback.
Examples abound. Think about it.
The linguistics scene has "descriptive grammarians" (currently in the
ascendant) versus "prescriptive grammarians" (started declining maybe 50
years ago). That's why I regularly find books, and even learned papers,
which confuse "throes" with "throws", "pour" with "pore", and many more,
since schools ceased to bother students with (horror!) rules,
substantive examinations etc.
To pull things together: my derivative/differential fusion is based
upon a return to fundamentals (mathematical and linguistic). I find
that this approach is superior to all others I've tried.
YMMV.
Geoff.