Symbolic differentiation of an arbitrary function

Asked Jul 24 '17 at 16:17

Active Jul 24 '17 at 16:47

Viewed 89 times

I often work with expressions in one or more arbitrary function, and would like to get simplified expressions for their derivatives.

For example I would like to define the normal to a graph as follows

and then compute symbolically its derivatives, and second derivatives etc. WITHOUT specifying the arbitrary function u.

Thank-you for any help.

PS. Apologies if my question has been asked before, I was not able to find an answer on the site yet.

EDIT: this is the error I get trying to naively differentiate

edited Jul 24 '17 at 16:47

asked Jul 24 '17 at 16:17

like: How to define a differential operator?? – Kuba Jul 24 '17 at 16:24
@Kuba thanks, but this seems to be something different, my main question is how to define and simplfy expressions in an arbitrary function (u in the above example). i am afraid it is quite an elementary question – Aerinmund Fagelson Jul 24 '17 at 16:33
I see, missed that. Try Block[{u}, n[x_, y_] = .... // SimplifyOrSomething notice no :=. – Kuba Jul 24 '17 at 16:35
What do you mean by symbolically computing derivatives without specifying u? What is wrong with D[n[x, y], x]? – Carl Woll Jul 24 '17 at 16:42
@CarlWoll I've tried this, see the error in my now editted answer. Kuba I am getting a similar error using Block – Aerinmund Fagelson Jul 24 '17 at 16:48
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This should be a duplicate. You want to do either Derivative[1,0][n][x,y] or something like Block[{x, y}, D[n[x,y], x]]. I prefer the former. – Carl Woll Jul 24 '17 at 16:52
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You have definitions for x and y lingering – Marius Ladegård Meyer Jul 24 '17 at 16:53
@CarlWoll thank-you, using block for {x,y} made a difference, but my result still has .5's floating around in all of the arguments, could you explain this? – Aerinmund Fagelson Jul 24 '17 at 16:56
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As @MariusLadegårdMeyer says, you have lingering definitions for x and y. Just Clear[x, y] and try again. – Carl Woll Jul 24 '17 at 16:58
Ah, many thanks for your help! I am still very much a novice with mathematica. – Aerinmund Fagelson Jul 24 '17 at 17:01

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