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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 849 "lndiff:=proc(f,x)\n
    local i;\n    if not has(f,x) then 0\n    elif f=x then 1/x\n    e
lif type(f,`+`) then diff(f,x)/f # 'lndiff'(f,x)\n    elif type(f,`*`)
 then \n      add(lndiff(op(i,f),x),i=1..nops(f))\n    elif type(f,`^`
) then \n      if not has(op(2,f),x) then op(2,f)*lndiff(op(1,f),x)\n \+
     else lndiff(exp(op(2,f)*ln(op(1,f))),x)\n      fi\n    elif type(
f,function) then\n      if op(0,f)=exp then diff(op(1,f),x)\n      eli
f op(0,f)=ln then diff(op(1,f),x)/op(1,f)/f\n      elif op(0,f)=sin th
en diff(op(1,f),x)*cot(op(1,f))\n      elif op(0,f)=cos then diff(op(1
,f),x)*tan(op(1,f))\n      elif op(0,f)=tan then lndiff(sin(op(1,f))/c
os(op(1,f)),x)\n      elif op(0,f)=GAMMA and nops(f)=1 then Psi(op(1,f
))\n      else ERROR(\"this case has not been implemented\",args)\n   \+
   fi\n    else ERROR(\"arguments do not match the definition\",args)
\n    fi\n  end:\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "f:=(x
^3+1)/(x-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG*&,&*$)%\"xG\"\"
$\"\"\"\"\"\"F,F,F+,&F)F,!\"\"F,!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "lndiff(f,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&*
$)%\"xG\"\"#\"\"\"F),&*$)F'\"\"$F)\"\"\"F.F.!\"\"F-*&F)F),&F'F.!\"\"F.
F/F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "f:=exp(x^2+x);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG-%$expG6#,&*$)%\"xG\"\"#\"\"\"\"
\"\"F+F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "lndiff(f,x);" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&%\"xG\"\"#\"\"\"F&" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "f:=ln((x^3+1)/(x-1));" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%\"fG-%#lnG6#*&,&*$)%\"xG\"\"$\"\"\"\"\"\"F/F/F
.,&F,F/!\"\"F/!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "lndi
ff(f,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&*&,&*&*$)%\"xG\"\"#\"\"
\"F+,&F)\"\"\"!\"\"F-!\"\"\"\"$*&,&*$)F)F0F+F-F-F-F+*$)F,\"\"#F+F/F.F-
F,F-F+*&F2\"\"\"-%#lnG6#*&F2F+F,F/\"\"\"F/" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 10 "f:=tan(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"f
G-%$tanG6#%\"xG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "lndiff(f
,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&-%$cotG6#%\"xG\"\"\"-%$tanGF
&!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "f:=GAMMA(2,exp(x)
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG*&-%$expG6#,$-F'6#%\"xG!\"
\"\"\"\",&F.F.F*F.F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "lnd
iff(f,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&-%$expG6#%\"xG!\"\"*&F$
\"\"\",&\"\"\"F,F$F,!\"\"F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
14 "trace(lndiff):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "lndif
f(1/cos(x),x);" }}{PARA 9 "" 1 "" {TEXT -1 37 "\{--> enter lndiff, arg
s = 1/cos(x), x" }}{PARA 9 "" 1 "" {TEXT -1 35 "\{--> enter lndiff, ar
gs = cos(x), x" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$tanG6#%\"xG" }}
{PARA 9 "" 1 "" {TEXT -1 41 "<-- exit lndiff (now in lndiff) = tan(x)
\}" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$-%$tanG6#%\"xG!\"\"" }}{PARA 
9 "" 1 "" {TEXT -1 45 "<-- exit lndiff (now at top level) = -tan(x)\}
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$-%$tanG6#%\"xG!\"\"" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "untrace(lndiff):" }}}}{MARK "14" 0 
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