higher derivatives of implicit equation?

[DrD]

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-

[Tim Wessman]

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.

[DrD]

Thank you kind sir. (I should have thought to try that!)
-Dale-

[melkhouly]

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

[Helge Gabert]

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

http://www.hpmuseum.org/forum/thread-857...light=xcas

[parisse]

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

[Helge Gabert]

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

[parisse]

I have edited the n=1 (default argument not available in current firmware).