{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 1 12 255 0 0 1 2 1 2 2 1 2 0 0 0 1 }{CSTYLE "_cstyle7" -1 203 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "_cstyle5" -1 206 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "_cstyle6" -1 210 "Courier" 1 12 255 0 0 1 2 1 2 2 1 2 0 0 0 1 }{PSTYLE "_pstyle10" -1 203 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "_pstyle8" -1 206 1 {CSTYLE "" -1 -1 "Courier" 1 12 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "_pstyle7" -1 207 1 {CSTYLE "" -1 -1 "Courier" 1 12 255 0 0 1 2 1 2 2 1 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "_pstyle6" -1 210 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "_pstyle9" -1 212 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }} {SECT 0 {EXCHG {PARA 210 "" 0 "" {TEXT 206 3 "01." }{TEXT 206 0 "" }}} {EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 210 14 "Dif:=proc(f,x)" } {MPLTEXT 1 210 1 "\n" }{MPLTEXT 1 210 11 "local F,y; " }{MPLTEXT 1 210 0 "" }{MPLTEXT 1 210 1 "\n" }{MPLTEXT 1 210 21 "if type(f,freeof(x )) " }{MPLTEXT 1 210 0 "" }{MPLTEXT 1 210 1 "\n" }{MPLTEXT 1 210 64 " \+ then return(0) #Differentiation von Konstanten" } {MPLTEXT 1 210 0 "" }{MPLTEXT 1 210 1 "\n" }{MPLTEXT 1 210 55 " elif \+ f=x then return(1) #Differentiation von x" }{MPLTEXT 1 210 0 " " }{MPLTEXT 1 210 1 "\n" }{MPLTEXT 1 210 43 " elif typematch(f,identi cal(x)^freeof(x)) " }{MPLTEXT 1 210 0 "" }{MPLTEXT 1 210 1 "\n" } {MPLTEXT 1 210 64 " then return (op(2,f)*op(1,f)^(op(2,f)-1)) \+ #Potenzregel" }{MPLTEXT 1 210 1 "\n" }{MPLTEXT 1 210 7 "end if;" } {MPLTEXT 1 210 0 "" }{MPLTEXT 1 210 1 "\n" }{MPLTEXT 1 210 60 "if type (f,'`+`') #Differentiation von Summen" }{MPLTEXT 1 210 0 "" }{MPLTEXT 1 210 1 "\n" }{MPLTEXT 1 210 34 " then return(map( y->Dif(y,x),f)) " }{MPLTEXT 1 210 0 "" }{MPLTEXT 1 210 1 "\n" } {MPLTEXT 1 210 7 "end if;" }{MPLTEXT 1 210 0 "" }{MPLTEXT 1 210 1 "\n " }{MPLTEXT 1 210 64 "if type(f,'`*`') #Differentiatio n von Produkten " }{MPLTEXT 1 210 0 "" }{MPLTEXT 1 210 1 "\n" } {MPLTEXT 1 210 73 " then return(op(1,f)*Dif(subsop(1=1,f),x)+subsop(1 =1,f)*Dif(op(1,f),x));" }{MPLTEXT 1 210 0 "" }{MPLTEXT 1 210 1 "\n" } {MPLTEXT 1 210 7 "end if;" }{MPLTEXT 1 210 0 "" }{MPLTEXT 1 210 1 "\n " }{MPLTEXT 1 210 58 "if type(f,'`^`') #Kettenregel f \374r Potenzen" }{MPLTEXT 1 210 1 "\n" }{MPLTEXT 1 210 78 " then retu rn(f*(Dif(op(2,f),x)*log(op(1,f))+op(2,f)*Dif(op(1,f),x)/op(1,f))) " } {MPLTEXT 1 210 1 "\n" }{MPLTEXT 1 210 7 "end if;" }{MPLTEXT 1 210 0 " " }{MPLTEXT 1 210 1 "\n" }{MPLTEXT 1 210 66 "if type(f,function) \+ #Kettenregel/spezielle Funktionen" }{MPLTEXT 1 210 1 "\n" } {MPLTEXT 1 210 19 " then F:=op(0,f); " }{MPLTEXT 1 210 1 "\n" } {MPLTEXT 1 210 74 " y:=op(1,f);\n if F=ln then return((1/y )*Dif(y,x))\n elif " }{MPLTEXT 1 210 34 "F=sin then return(cos(y )*Dif(y,x))" }{MPLTEXT 1 210 1 "\n" }{MPLTEXT 1 210 2 " " }{MPLTEXT 1 210 5 " " }{MPLTEXT 1 210 40 "elif F=cos then return(-sin(y)*Dif (y,x))" }{MPLTEXT 1 210 1 "\n" }{MPLTEXT 1 210 54 " elif F=tan t hen return((1+(tan(y))^2)*Dif(y,x))" }{MPLTEXT 1 210 1 "\n" }{MPLTEXT 1 210 58 " elif F=arcsin then return(1/(sqrt(1-y^2))*Dif(y,x))" }{MPLTEXT 1 210 1 "\n" }{MPLTEXT 1 210 52 " elif F=arctan then r eturn(1/(1+y^2)*Dif(y,x))" }{MPLTEXT 1 210 1 "\n" }{MPLTEXT 1 210 46 " elif F=exp then return(exp(y)*Dif(y,x))" }{MPLTEXT 1 210 7 " \+ " }{MPLTEXT 1 210 1 "\n" }{MPLTEXT 1 210 14 " end if;" } {MPLTEXT 1 210 8 " " }{MPLTEXT 1 210 0 "" }{MPLTEXT 1 210 1 "\n " }{MPLTEXT 1 210 7 "end if;" }{MPLTEXT 1 210 0 "" }{MPLTEXT 1 210 1 " \n" }{MPLTEXT 1 210 11 "'Dif(f,x)';" }{MPLTEXT 1 210 0 "" }{MPLTEXT 1 210 1 "\n" }{MPLTEXT 1 210 9 "end proc:" }{MPLTEXT 1 210 0 "" }}} {EXCHG {PARA 210 "" 0 "" {TEXT 206 3 "02." }{TEXT 206 0 "" }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 0 11 "Dif(x^3,x);" }{MPLTEXT 1 0 0 "" } }}{EXCHG {PARA 210 "" 0 "" {TEXT 206 3 "03." }{TEXT 206 0 "" }}} {EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 210 15 "Dif(sqrt(x),x);" } {MPLTEXT 1 210 0 "" }}}{EXCHG {PARA 210 "" 0 "" {TEXT 206 3 "06." } {TEXT 206 0 "" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 210 13 "Dif(3* x^2,x);" }{MPLTEXT 1 210 0 "" }}}{EXCHG {PARA 210 "" 0 "" {TEXT 206 3 "07." }{TEXT 206 0 "" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 210 26 "Dif(sum(k*x^k,k=0..10),x);" }{MPLTEXT 1 210 0 "" }}}{EXCHG {PARA 210 "" 0 "" {TEXT 206 3 "11." }{TEXT 206 0 "" }}}{EXCHG {PARA 207 "> " 0 " " {MPLTEXT 1 210 23 "Dif((x^2+3)*(3*x+2),x);" }{MPLTEXT 1 210 0 "" }}} {EXCHG {PARA 210 "" 0 "" {TEXT 206 3 "15." }{TEXT 206 0 "" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 210 16 "Dif(sin(x^2),x);" }{MPLTEXT 1 210 0 "" }}}{EXCHG {PARA 210 "" 0 "" {TEXT 206 3 "18." }{TEXT 206 0 " " }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 210 22 "Dif((1+x^2)^sin(x), x);" }{MPLTEXT 1 210 0 "" }}}{EXCHG {PARA 210 "" 0 "" {TEXT 206 3 "19. " }{TEXT 206 0 "" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 210 14 "Dif (exp(x),x);" }{MPLTEXT 1 210 0 "" }}}{EXCHG {PARA 210 "" 0 "" {TEXT 206 3 "20." }{TEXT 206 0 "" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 210 23 "Dif((x^2+3)/(3*x+2),x);" }{MPLTEXT 1 210 0 "" }}}{EXCHG {PARA 210 "" 0 "" {TEXT 206 3 "21." }{TEXT 206 0 "" }}}{EXCHG {PARA 207 "> \+ " 0 "" {MPLTEXT 1 210 55 "Dif(log(sin(x))/arcsin(x)+arctan(1/x)*tan(x) /log(x),x);" }{MPLTEXT 1 210 0 "" }}}{PARA 212 "" 0 "" {TEXT 203 0 "" }}{PARA 203 "" 0 "" {TEXT -1 0 "" }}}{MARK "1 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }