Implicit derivatives in one line. How do I do it?

Question

I have this little script to derive implicitly

$PrePrint = # /. {D[y_, x_, NonConstants -> {y_}] :> y'[x]} &;

Example:

D[x == y^3 + x y, x, NonConstants -> y]

1 == y + x y'[x] + 3 y^2*y'[x]

and then, to obtain the expression for y'[x], I use

Solve[1 == y + x y'[x] + 3 y^2*y'[x],y'[x]] //FullSimplify

How can I get all these steps in one line?

I'd like to have something like

$PrePrint = # /. {D[y_, x_, NonConstants -> {y_}] :> y'[x]} &; //Solve...

If I saw that, but I want to publish online with the Solve not like having to go to take the result of the derivative and clearance and y '[x] — Fernando Silva, Jul 06 '15 at 01:02
I cannot understand the question at all. You may need a better english translation before posting here. — Jens, Jul 06 '15 at 01:19

Karsten7 · Accepted Answer · 2015-07-06T16:25:12.377

3

If my interpretation of your question is correct, the following code should produce the desired behaviour.

prePrint[input_] := 
  Module[{solveFor}, 
   input /. {D[y_, x_, NonConstants -> {y_}] :> (solveFor = y'[x])} //
      If[OwnValues[solveFor] === {}, input, Solve[#, solveFor]] & // 
    FullSimplify];
$PrePrint = prePrint;

Test

D[x == y^3 + x y, x, NonConstants -> y]

{{y'[x]] -> (1 - y)/(x + 3 y^2)}}

edited Jul 06 '15 at 16:25

answered Jul 06 '15 at 01:54

Karsten7

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if just that is, thank you, sorry for my English – Fernando Silva Jul 06 '15 at 02:02

Implicit derivatives in one line. How do I do it?

1 Answers1