I agree with the idea that one ought to specify what variable is
being held in a partial derivative if there is any possibility of
confusion.
eg. for f(x,y) we might want the partial of f with respect to x while
y is held fixed which we would write as (curly-d f / curly-d x)
subscript{y}
Fine. Or maybe you prefer no parentheses, but instead a vertical bar
separating the derivative and the subscript. But how would you write
some harder cases? Here are two for example:
1. partial of (f/y) with respect to y while x is held fixed -
specifically, where would you put the parentheses? I've seen people
put the curly-d/curly-d x outside the parentheses in this case. I
suppose one could put brackets and parentheses, but that starts to
get ugly.
2. a second partial: say you first differentiate f with respect to x
while y is held fixed, then differentiate with respect to y while x
is held fixed - where now will you put parentheses and subscripts?
These are just warmup examples. You can probably come up with much
more gnarly examples. For example, maybe I want to specify that one
is to substitute in some value such as x0 for x at some point along
the way (say I have 3 variables x,y,x).
--
Carl E Mungan, Assoc Prof of Physics 410-293-6680 (O) -3729 (F)
Naval Academy Stop 9c, 572C Holloway Rd, Annapolis MD 21402-1363 mailto:mungan@usna.eduhttp://usna.edu/Users/physics/mungan/