Fwd: Help differentiating composite functions

-----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