Function: derivnum
Section: sums
C-Name: derivnum0
Prototype: V=GEp
Help: derivnum(X=a,expr): numerical derivation of expr with respect to
 X at X = a.
Wrapper: (,Gp)
Description:
  (gen,gen):gen:prec derivnum(${2 cookie}, ${2 wrapper}, $1, prec)
Doc: numerical derivation of \var{expr} with respect to $X$ at $X=a$.

 \bprog
 ? derivnum(x=0,sin(exp(x))) - cos(1)
 %1 = -1.262177448 E-29
 @eprog
 A clumsier approach, which would not work in library mode, is
 \bprog
 ? f(x) = sin(exp(x))
 ? f'(0) - cos(1)
 %1 = -1.262177448 E-29
 @eprog
 When $a$ is a power series, compute \kbd{derivnum(t=a,f)} as $f'(a) =
 (f(a))'/a'$.

 \synt{derivnum}{void *E, GEN (*eval)(void*,GEN), GEN a, long prec}. Also
 available is \fun{GEN}{derivfun}{void *E, GEN (*eval)(void *, GEN), GEN a, long prec}, which also allows power series for $a$.

Function: _derivfun
Section: programming/internals
C-Name: derivfun0
Prototype: GGp
Help: _derivfun(closure,[args]) numerical derivation of closure with respect to
 the first variable at (args).