higher derivatives of implicit equation?
09-16-2017, 11:33 AM (This post was last modified: 09-16-2017 05:20 PM by DrD.)
Post: #1
 DrD Senior Member Posts: 969 Joined: Feb 2014
higher derivatives of implicit equation?
Can higher order derivatives be obtained in CAS, (without programming)?

Example:
z:=(3*x^2-y^2) = 16,
simplify(implicit_diff(z,x,y))
leads to 3*x /y as the first derivative of z.

How would one obtain the (Second derivative): d^2y/dx^2=(3*y-3*x*3*x/y)/y^2 (or simplified equivalent)?

-Dale-
09-16-2017, 05:52 PM
Post: #2
 Tim Wessman Senior Member Posts: 1,854 Joined: Dec 2013
RE: higher derivatives of implicit equation?
simplify(implicit_diff(z,x,y,2)) works for me on the latest version. So next update (if any) should have it being very simple at least.

TW

Although I work for the HP calculator group, the views and opinions I post here are my own.
09-16-2017, 07:13 PM
Post: #3
 DrD Senior Member Posts: 969 Joined: Feb 2014
RE: higher derivatives of implicit equation?
Thank you kind sir. (I should have thought to try that!)
-Dale-
09-18-2017, 10:00 AM
Post: #4
 melkhouly Junior Member Posts: 3 Joined: Jan 2016
RE: higher derivatives of implicit equation?
I have tried that on my Prime with software 2017 07 10 (12066) and cas 1.1.2-11
and the command implicit_diff(z,x,y,2) gace Error Bad Argument Value
09-18-2017, 09:17 PM (This post was last modified: 09-18-2017 09:21 PM by Helge Gabert.)
Post: #5
 Helge Gabert Senior Member Posts: 449 Joined: Dec 2013
RE: higher derivatives of implicit equation?
Yes, we mere mortals will have to wait for the next firmware update (if any!) . . . maybe more XCAS commands will be implemented as well, as discussed here

09-19-2017, 06:04 AM (This post was last modified: 09-21-2017 12:37 PM by parisse.)
Post: #6
 parisse Senior Member Posts: 846 Joined: Dec 2013
RE: higher derivatives of implicit equation?
In the meantime, you can enter this program:
Code:
 idiff(eq,x,y,n):=begin   local j,dn,d1;   d1:=-diff(eq,x)/diff(eq,y);   dn:=d1;   for j from 2 to n do     dn:=diff(dn,x)+diff(dn,y)*d1;   end;   return dn; end
09-20-2017, 02:32 PM
Post: #7
 Helge Gabert Senior Member Posts: 449 Joined: Dec 2013
RE: higher derivatives of implicit equation?
Great! Just two minor modifications. In order to run on the Prime current firmware,

1) n=1 in the first line gives an error message "unable to eval test in loop . . . " and ought to be replaced by n

2) eq should not be entered as an equation, but as an expression, in order to avoid the =undef
09-21-2017, 12:38 PM
Post: #8
 parisse Senior Member Posts: 846 Joined: Dec 2013
RE: higher derivatives of implicit equation?
I have edited the n=1 (default argument not available in current firmware).
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