Clearing Problem with DSolve

Question

Consider:

This is a classic mistake (using a single equal sign) that has been discussed on Mathematica Stack Exchange before. I know that Clear[Derivative] will cure the problem. However, consider the following.

?f' does not reveal anything in the global workspace. Neither does ?f'[x]. Yet f'[x]=. clears the problem, so I believe something is stored in f'[x] but why can't I see it with the question mark process. Any way to see it?

Since the value is mistakenly assigned to Derivative, does ?Derivative contain that information? — MarcoB, Apr 17 '16 at 06:23
@MarcoB After entering Clear[f, x] and DSolve[{f'[x]=8x^3+12x+3,f[1]==6]},f[x],x], entering ?Derivative just brings up instructions for the Derivative command, not the content of f'[x]. — David, Apr 17 '16 at 15:00
Related: Error entering equation in DSolve, which is your old question :) Halirutan's answer there answers this question, doesn't it? — Michael E2, Apr 17 '16 at 19:14
@MichaelE2 Thanks for pointing out the old question. Been a while. I have trouble searching through all the old questions I've asked. How do you find them so quickly? And, thanks for all the tremendous help you've given me over the years. — David, Apr 18 '16 at 22:26

score 1 · Answer 1 · edited Apr 13 '17 at 12:55

After some searching, it turns out that you can obtain those definitions using SubValues:

Clear[f, x]
f'[x] = 3 x

SubValues[Derivative]

(* Out: {HoldPattern[Derivative[1][f][x]] :> 3 x} *)

As mentioned in this answer, SubValues is used for definitions of the following type:

d[e][f] = something;

As you know, f'[x] is really interpreted as Derivative[1][f][x], so setting f'[x] = something generates a SubValue for Derivative.

Adapting a phrase from the linked answer: "This defines neither an OwnValue nor a DownValue for Derivative, since it does not really define the value for the atomic object Derivative itself, but for Derivative[1][f], which is a composite."

Clearing Problem with DSolve

1 Answers1