Fwd: Help differentiating composite functions
- Subject: Fwd: Help differentiating composite functions
- From: Jeffrey Hankins
- Date: Wed, 30 Jun 2010 01:54:21 -0400
It works with pdiff. Thanks a lot.
On Tue, Jun 29, 2010 at 19:23, Barton Willis <willisb at unk.edu> wrote:
>
> -----maxima-bounces at math.utexas.edu wrote: -----
>
>
> >In 2002 Barton started to write a replacement for ndiff, called pdiff,
>
> To use pdiff, just load it. Examples:
>
> (%i1) load(pdiff)$
>
> (%i2) taylor(f(x),x,0,1);
> (%o2)/T/ f(0)+f[(1)](0)*x+...
>
> (%i3) -diff(f(x),x,2)/2 + (x^2/2 -e ) * f(x);
> (%o3) (x^2/2-e)*f(x)-f[(2)](x)/2
>
> (%i4) %, f(x) := g(x^2);
> (%o4) (x^2/2-e)*g(x^2)-(4*x^2*g[(2)](x^2)+2*g[(1)](x^2))/2
>
> (%i5) ratsubst(x,x^2,%);
> (%o5) -(4*x*g[(2)](x)+2*g[(1)](x)+(2*e-x)*g(x))/2
>
> (%i6) solve(%,diff(g(x),x,2));
> (%o6) [g[(2)](x)=-(2*g[(1)](x)+(2*e-x)*g(x))/(4*x)]
>
>
> --Barton
>