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+--- Thread: higher derivatives of implicit equation? (/thread-9091.html)
higher derivatives of implicit equation? - DrD - 09-16-2017 11:33 AM
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-
RE: higher derivatives of implicit equation? - Tim Wessman - 09-16-2017 05:52 PM
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.
RE: higher derivatives of implicit equation? - DrD - 09-16-2017 07:13 PM
Thank you kind sir. (I should have thought to try that!)
-Dale-
RE: higher derivatives of implicit equation? - melkhouly - 09-18-2017 10:00 AM
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
RE: higher derivatives of implicit equation? - Helge Gabert - 09-18-2017 09:17 PM
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-8577.html?highlight=xcas
RE: higher derivatives of implicit equation? - parisse - 09-19-2017 06:04 AM
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;
endRE: higher derivatives of implicit equation? - Helge Gabert - 09-20-2017 02:32 PM
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
RE: higher derivatives of implicit equation? - parisse - 09-21-2017 12:38 PM
I have edited the n=1 (default argument not available in current firmware).