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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 14 "Jacobimatricer" }}{PARA 
0 "" 0 "" {TEXT 256 31 "Al anvendelse er p\345 eget ansvar" }{TEXT -1 
1 "." }{MPLTEXT 1 0 0 "" }}{PARA 0 "" 0 "" {TEXT -1 1 " " }{MPLTEXT 1 
0 0 "" }}{PARA 0 "" 0 "" {TEXT -1 41 "Vejledning:\n1) Udfyld v\346rdie
r for opgaven" }}{PARA 0 "" 0 "" {TEXT -1 53 "2) G\345 til bunden af m
aple-arket og tryk \"!!!\"-knappen" }{MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 41 "-- Hvilke variabl
e er der i funktionerne?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 
"args:=[x,y];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%argsG7$%\"xG%\"yG
" }}}{EXCHG {PARA 257 "" 0 "" {TEXT -1 21 "-- Skriv funktionen f" }
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "f:=[x^2
-y, y^2+x];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG7$,&*$)%\"xG\"\"#
\"\"\"F+%\"yG!\"\",&*$)F,F*F+F+F)F+" }}}{EXCHG {PARA 258 "" 0 "" 
{TEXT -1 21 "-- Skriv funktionen g" }{MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "g:=[x+y,x-y];" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"gG7$,&%\"xG\"\"\"%\"yGF(,&F'F(F)!\"\"" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 23 "Jacobimatricen for f er" }{MPLTEXT 1 0 0 
"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "Df:=jacobian(f, args);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#DfGK%'matrixG6#7$7$,$*&\"\"#\"
\"\"%\"xGF-F-!\"\"7$F-,$*&F,F-%\"yGF-F-Q(pprint06\"" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 23 "Jacobimatricen for g er" }{MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "Dg:=jacobian(g, args);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#DgGK%'matrixG6#7$7$\"\"\"F*7$F*!\"
\"Q(pprint06\"" }}}{EXCHG {PARA 259 "" 0 "" {TEXT -1 56 "-- Vi \370nsk
er at finde  D(g o f)(a), hvor a defineres til" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 9 "a:=[1,1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%
\"aG7$\"\"\"F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 103 "Vi deler opgav
en op i \nD(g o f)(a) = Dg(f(a)) * Df(a) = Dg(b) * Df(a)\nS\345ledes f
inder vi f\370rst b = f(a):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
27 "b:=subs(x=a[1], y=a[2], f);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%
\"bG7$\"\"!\"\"#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 16 "Df(a) findes \+
til" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "D
fa:=subs(x=a[1], y=a[2], jacobian(f,args));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$DfaGK%'matrixG6#7$7$\"\"#!\"\"7$\"\"\"F*Q(pprint06\"
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 16 "Dg(b) findes til" }{MPLTEXT 
1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "Dgb:=subs(x=b[1]
, y=b[2], jacobian(g,args));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$Dgb
GK%'matrixG6#7$7$\"\"\"F*7$F*!\"\"Q(pprint06\"" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 41 "Da er D(g o f)(a) = Dg(b) * Df(a), som er" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "multiply(subs(x=b[1], y=b[2]
, jacobian(g,args)), subs(x=a[1], y=a[2], jacobian(f,args)));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#K%'matrixG6#7$7$\"\"$\"\"\"7$F)!\"$Q(p
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