Abstract
is unlikely to occur. However, a situation in which a student actually did something equivalent on a test is related in [4], and is addressed in slightly greater generality in [1]. The standard sum, product, and quotient rules from differential calculus also lend themselves to a similar interpretation: To differentiate f (x)g(x) (or f (x) + g(x) or f (x) / g (x)), first differentiate as if g(x) was constant, then as if f (x) was constant; add the results. Indeed, a function f(x) which is comprised of an algebraic combination of an arbitrary number of simpler functions f (x) can be differentiated in this way, differentiating as if all the fj are constant except for fi; repeat for all fj; add the results.
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