83:@0.904366:0.963104:0.932133:0.963104:0.932133:0.941283:0.904366:0.941283:0.000000:0.000000
Matemática:@0.795130:0.956142:0.879896:0.956142:0.879896:0.943479:0.795130:0.943479:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3.º BG:@0.837761:0.967458:0.879897:0.967458:0.879897:0.954794:0.837761:0.954794:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2.:@0.096359:0.277205:0.110585:0.277205:0.110585:0.260304:0.096359:0.260304:0.000000:0.000000
  La derivada geométrica representa la pendiente de la recta tangente en un pun-:@0.110585:0.277205:0.712467:0.277205:0.712467:0.260816:0.110585:0.260816:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
to. Vamos a hallar la ecuación de la recta tangente a la curva en un punto.:@0.124848:0.293801:0.662633:0.293801:0.662633:0.277412:0.124848:0.277412:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.096359:0.321088:0.100395:0.321088:0.100395:0.304699:0.096359:0.304699:0.000000
Sea la función  ():@0.124848:0.321088:0.261958:0.321129:0.261958:0.304740:0.124848:0.304699:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
fx:@0.233930:0.321129:0.255269:0.321129:0.255269:0.304767:0.233930:0.304767:0.000000:0.000000
x:@0.279372:0.321129:0.286835:0.321129:0.286835:0.304767:0.279372:0.304767:0.000000
x:@0.320834:0.321129:0.328298:0.321129:0.328298:0.304767:0.320834:0.304767:0.000000
=:@0.264925:0.320714:0.275042:0.320714:0.275042:0.303771:0.264925:0.303771:0.000000
+:@0.298334:0.320714:0.308451:0.320714:0.308451:0.303771:0.298334:0.303771:0.000000
2:@0.288427:0.313468:0.293639:0.313468:0.293639:0.303969:0.288427:0.303969:0.000000
3 . Hallamos la derivada en   = 1.:@0.311043:0.321129:0.555716:0.321090:0.555716:0.304701:0.311043:0.304740:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.517000:0.321090:0.524463:0.321090:0.524463:0.304728:0.517000:0.304728:0.000000
Paso 1. :@0.102121:0.344421:0.156516:0.344421:0.156516:0.328843:0.102121:0.328843:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para obtener el punto :@0.155277:0.344421:0.300185:0.344421:0.300185:0.329522:0.155277:0.329522:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de tangencia, reemplazamos  tangente es la derivada de :@0.102121:0.359509:0.487883:0.359509:0.487883:0.344610:0.102121:0.344610:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.102121:0.374596:0.108906:0.374596:0.108906:0.359723:0.102121:0.359723:0.000000
 = 1 en la función.:@0.108906:0.374596:0.227714:0.374596:0.227714:0.359697:0.108906:0.359697:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
fx:@0.103995:0.393177:0.121919:0.393177:0.121919:0.379106:0.103995:0.379106:0.000000:0.000000
x:@0.142166:0.393177:0.148435:0.393177:0.148435:0.379106:0.142166:0.379106:0.000000
x f:@0.176994:0.393177:0.200028:0.393177:0.200028:0.379106:0.176994:0.379106:0.000000:0.000000:0.000000
P:@0.104211:0.411993:0.111579:0.411993:0.111579:0.397923:0.104211:0.397923:0.000000
():@0.110062:0.393177:0.127538:0.393177:0.127538:0.379082:0.110062:0.379082:0.000000:0.000000
;( ) 1:@0.184517:0.393177:0.235067:0.393177:0.235067:0.379082:0.184517:0.379082:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(, ):@0.111951:0.411993:0.141779:0.411993:0.141779:0.397899:0.111951:0.397899:0.000000:0.000000:0.000000:0.000000
=:@0.130031:0.392820:0.138529:0.392820:0.138529:0.378250:0.130031:0.378250:0.000000
+:@0.158094:0.392820:0.166593:0.392820:0.166593:0.378250:0.158094:0.378250:0.000000
=+:@0.217535:0.392820:0.249515:0.392820:0.249515:0.378250:0.217535:0.378250:0.000000:0.000000
():@0.260150:0.394325:0.276171:0.394325:0.276171:0.375704:0.260150:0.375704:0.000000:0.000000
=:@0.278839:0.392820:0.287338:0.392820:0.287338:0.378250:0.278839:0.378250:0.000000
2:@0.149772:0.386587:0.154150:0.386587:0.154150:0.378419:0.149772:0.378419:0.000000
2:@0.232708:0.386587:0.237086:0.386587:0.237086:0.378419:0.232708:0.378419:0.000000
3:@0.168770:0.393177:0.176323:0.393177:0.176323:0.379082:0.168770:0.379082:0.000000
1:@0.205579:0.393177:0.213133:0.393177:0.213133:0.379082:0.205579:0.379082:0.000000
3 1:@0.251707:0.393177:0.272666:0.393177:0.272666:0.379082:0.251707:0.379082:0.000000:0.000000:0.000000
4:@0.290266:0.393177:0.297820:0.393177:0.297820:0.379082:0.290266:0.379082:0.000000
14:@0.115382:0.411993:0.137223:0.411993:0.137223:0.397899:0.115382:0.397899:0.000000:0.000000
  :@0.189310:0.393177:0.196090:0.393177:0.196090:0.379082:0.189310:0.379082:0.000000:0.000000
 :@0.125288:0.411993:0.128678:0.411993:0.128678:0.397899:0.125288:0.397899:0.000000
Paso 2.:@0.307898:0.344421:0.360149:0.344421:0.360149:0.328843:0.307898:0.328843:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.360149:0.344421:0.363818:0.344421:0.363818:0.329522:0.360149:0.329522:0.000000
La pendiente de la :@0.363818:0.344421:0.491268:0.344421:0.491268:0.329522:0.363818:0.329522:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la función evaluada en   = 1.  la tangente empleamos la :@0.307898:0.374596:0.691099:0.374596:0.691099:0.359697:0.307898:0.359697:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.462102:0.374596:0.468887:0.374596:0.468887:0.359723:0.462102:0.359723:0.000000
Aplicamos propiedades.:@0.307898:0.389684:0.468351:0.389684:0.468351:0.374785:0.307898:0.374785:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
fx:@0.310109:0.408508:0.328888:0.408508:0.328888:0.394111:0.310109:0.394111:0.000000:0.000000
x:@0.350099:0.408508:0.356667:0.408508:0.356667:0.394111:0.350099:0.394111:0.000000
x:@0.386586:0.408508:0.393153:0.408508:0.393153:0.394111:0.386586:0.394111:0.000000
fx:@0.413667:0.408508:0.436678:0.408508:0.436678:0.394111:0.413667:0.394111:0.000000:0.000000
x:@0.465267:0.408508:0.471835:0.408508:0.471835:0.394111:0.465267:0.394111:0.000000
m:@0.310336:0.426764:0.323212:0.426764:0.323212:0.412367:0.310336:0.412367:0.000000
():@0.316466:0.408508:0.334775:0.408508:0.334775:0.394086:0.316466:0.394086:0.000000:0.000000
;    :@0.394467:0.408508:0.413689:0.408508:0.413689:0.394086:0.394467:0.394086:0.000000:0.000000:0.000000:0.000000:0.000000
’() 2:@0.421516:0.408508:0.464565:0.408508:0.464565:0.394086:0.421516:0.394086:0.000000:0.000000:0.000000:0.000000:0.000000
() 35:@0.363915:0.426764:0.420516:0.426764:0.420516:0.412342:0.363915:0.412342:0.000000:0.000000:0.000000:0.000000:0.000000
(, ):@0.327202:0.428528:0.343602:0.428528:0.343602:0.420169:0.327202:0.420169:0.000000:0.000000:0.000000:0.000000
=:@0.337382:0.408143:0.346285:0.408143:0.346285:0.393234:0.337382:0.393234:0.000000
+:@0.366783:0.408143:0.375685:0.408143:0.375685:0.393234:0.366783:0.393234:0.000000
=:@0.445184:0.408143:0.454087:0.408143:0.454087:0.393234:0.445184:0.393234:0.000000
+:@0.475460:0.408143:0.484363:0.408143:0.484363:0.393234:0.475460:0.393234:0.000000
=:@0.345353:0.426399:0.354256:0.426399:0.354256:0.411490:0.345353:0.411490:0.000000
+ =:@0.379489:0.426399:0.410040:0.426399:0.410040:0.411490:0.379489:0.411490:0.000000:0.000000:0.000000
2:@0.358068:0.401766:0.362655:0.401766:0.362655:0.393408:0.358068:0.393408:0.000000
14:@0.329827:0.428528:0.340315:0.428528:0.340315:0.420169:0.329827:0.420169:0.000000:0.000000
3:@0.377970:0.408508:0.385884:0.408508:0.385884:0.394086:0.377970:0.394086:0.000000
3:@0.486646:0.408508:0.494560:0.408508:0.494560:0.394086:0.486646:0.394086:0.000000
21:@0.356818:0.426764:0.375419:0.426764:0.375419:0.412342:0.356818:0.412342:0.000000:0.000000
Paso 3.:@0.513676:0.344421:0.565927:0.344421:0.565927:0.328843:0.513676:0.328843:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Para determinar la :@0.565927:0.344421:0.694064:0.344421:0.694064:0.329522:0.565927:0.329522:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ecuación de :@0.513676:0.359509:0.599214:0.359509:0.599214:0.344610:0.513676:0.344610:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
expresión punto pendiente.:@0.513676:0.389684:0.699222:0.389684:0.699222:0.374785:0.513676:0.374785:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
yy:@0.517362:0.408869:0.546519:0.408869:0.546519:0.394471:0.517362:0.394471:0.000000:0.000000
mx x:@0.566238:0.408869:0.616525:0.408869:0.616525:0.394471:0.566238:0.394471:0.000000:0.000000:0.000000:0.000000
y:@0.517362:0.428129:0.523946:0.428129:0.523946:0.413731:0.517362:0.413731:0.000000
x:@0.574119:0.428129:0.580686:0.428129:0.580686:0.413731:0.574119:0.413731:0.000000
y:@0.619768:0.428129:0.626352:0.428129:0.626352:0.413731:0.619768:0.413731:0.000000
x:@0.650352:0.428129:0.656919:0.428129:0.656919:0.413731:0.650352:0.413731:0.000000
−:@0.527544:0.408504:0.536447:0.408504:0.536447:0.393595:0.527544:0.393595:0.000000
=:@0.554544:0.408504:0.563447:0.408504:0.563447:0.393595:0.554544:0.393595:0.000000
−:@0.597793:0.408504:0.606696:0.408504:0.606696:0.393595:0.597793:0.393595:0.000000
(:@0.580155:0.410044:0.585555:0.410044:0.585555:0.390991:0.580155:0.390991:0.000000
):@0.622544:0.410044:0.627944:0.410044:0.627944:0.390991:0.622544:0.390991:0.000000
−=:@0.527544:0.427763:0.558841:0.427763:0.558841:0.412854:0.527544:0.412854:0.000000:0.000000
−:@0.584301:0.427763:0.593204:0.427763:0.593204:0.412854:0.584301:0.412854:0.000000
=:@0.630501:0.427763:0.639404:0.427763:0.639404:0.412854:0.630501:0.412854:0.000000
−:@0.660550:0.427763:0.669453:0.427763:0.669453:0.412854:0.660550:0.412854:0.000000
1:@0.546616:0.410633:0.551203:0.410633:0.551203:0.402274:0.546616:0.402274:0.000000
1:@0.616642:0.410633:0.621228:0.410633:0.621228:0.402274:0.616642:0.402274:0.000000
45(:@0.538969:0.428129:0.572569:0.428129:0.572569:0.413706:0.538969:0.413706:0.000000:0.000000:0.000000
1);   :@0.594202:0.428129:0.619775:0.428129:0.619775:0.413706:0.594202:0.413706:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.641975:0.428129:0.649889:0.428129:0.649889:0.413706:0.641975:0.413706:0.000000
1:@0.670451:0.428129:0.678365:0.428129:0.678365:0.413706:0.670451:0.413706:0.000000
a):@0.124851:0.588374:0.139759:0.588374:0.139759:0.571473:0.124851:0.571473:0.000000:0.000000
 :@0.139759:0.588374:0.143795:0.588374:0.143795:0.571985:0.139759:0.571985:0.000000
fx:@0.155832:0.588302:0.176957:0.588302:0.176957:0.572431:0.155832:0.572431:0.000000:0.000000
x:@0.216108:0.588302:0.223496:0.588302:0.223496:0.572431:0.216108:0.572431:0.000000
fx:@0.155832:0.618030:0.181719:0.618030:0.181719:0.602160:0.155832:0.602160:0.000000:0.000000
x:@0.231961:0.618030:0.239350:0.618030:0.239350:0.602160:0.231961:0.602160:0.000000
d:@0.282076:0.609525:0.291252:0.609525:0.291252:0.593655:0.282076:0.593655:0.000000
dx:@0.278245:0.628548:0.294755:0.628548:0.294755:0.612678:0.278245:0.612678:0.000000:0.000000
x:@0.315771:0.618030:0.323160:0.618030:0.323160:0.602160:0.315771:0.602160:0.000000
fx:@0.155832:0.649168:0.181719:0.649168:0.181719:0.633297:0.155832:0.633297:0.000000:0.000000
x:@0.231961:0.649168:0.239350:0.649168:0.239350:0.633297:0.231961:0.633297:0.000000
fx:@0.155832:0.674053:0.181719:0.674053:0.181719:0.658183:0.155832:0.658183:0.000000:0.000000
():@0.162983:0.588302:0.183580:0.588302:0.183580:0.572405:0.162983:0.572405:0.000000:0.000000
’( ) 42:@0.164643:0.618030:0.231180:0.618031:0.231180:0.602134:0.164643:0.602133:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
’( ) 42:@0.164643:0.649168:0.231180:0.649168:0.231180:0.633271:0.164643:0.633270:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
’( ) 82:@0.164643:0.674053:0.230614:0.674054:0.230614:0.658156:0.164643:0.658156:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.186517:0.587899:0.196533:0.587899:0.196533:0.571465:0.186517:0.571465:0.000000
+:@0.227565:0.587899:0.237580:0.587899:0.237580:0.571465:0.227565:0.571465:0.000000
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):@0.245957:0.589596:0.252032:0.589596:0.252032:0.568594:0.245957:0.568594:0.000000
=:@0.191281:0.617627:0.201297:0.617627:0.201297:0.601193:0.191281:0.601193:0.000000
+:@0.243421:0.617627:0.253436:0.617627:0.253436:0.601193:0.243421:0.601193:0.000000
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):@0.261816:0.619324:0.267891:0.619324:0.267891:0.598321:0.261816:0.598321:0.000000
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=:@0.191281:0.648764:0.201297:0.648764:0.201297:0.632330:0.191281:0.632330:0.000000
+:@0.243421:0.648764:0.253436:0.648764:0.253436:0.632330:0.243421:0.632330:0.000000
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=:@0.191281:0.673651:0.201297:0.673651:0.201297:0.657217:0.191281:0.657217:0.000000
2:@0.206423:0.588302:0.215326:0.588302:0.215326:0.572405:0.206423:0.572405:0.000000
1:@0.239024:0.588302:0.247927:0.588302:0.247927:0.572405:0.239024:0.572405:0.000000
1:@0.254878:0.618031:0.263781:0.618031:0.263781:0.602134:0.254878:0.602134:0.000000
2:@0.306087:0.618031:0.314990:0.618031:0.314990:0.602134:0.306087:0.602134:0.000000
1:@0.338688:0.618031:0.347590:0.618031:0.347590:0.602134:0.338688:0.602134:0.000000
12:@0.254878:0.649168:0.285454:0.649168:0.285454:0.633271:0.254878:0.633271:0.000000:0.000000
4:@0.252386:0.579002:0.257545:0.579002:0.257545:0.569789:0.252386:0.569789:0.000000
3:@0.267938:0.608733:0.273098:0.608733:0.273098:0.599520:0.267938:0.599520:0.000000
3:@0.267938:0.639871:0.273098:0.639871:0.273098:0.630658:0.267938:0.630658:0.000000
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3:@0.267364:0.664754:0.272524:0.664754:0.272524:0.655541:0.267364:0.655541:0.000000
a):@0.124851:0.722866:0.139759:0.722866:0.139759:0.705966:0.124851:0.705966:0.000000:0.000000
  Hallamos la derivada por producto en   = 1.:@0.139759:0.722866:0.472983:0.722866:0.472983:0.706477:0.139759:0.706477:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
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x:@0.258432:0.746418:0.265597:0.746418:0.265597:0.730711:0.258432:0.730711:0.000000
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fx:@0.155756:0.777579:0.180859:0.777579:0.180859:0.761873:0.155756:0.761873:0.000000:0.000000
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x:@0.284915:0.777579:0.292080:0.777579:0.292080:0.761873:0.284915:0.761873:0.000000
x:@0.324170:0.777579:0.331335:0.777579:0.331335:0.761873:0.324170:0.761873:0.000000
x:@0.385326:0.777579:0.392491:0.777579:0.392491:0.761873:0.385326:0.761873:0.000000
x:@0.424582:0.777579:0.431746:0.777579:0.431746:0.761873:0.424582:0.761873:0.000000
d:@0.469657:0.769162:0.478555:0.769162:0.478555:0.753455:0.469657:0.753455:0.000000
dx:@0.465942:0.787989:0.481952:0.787989:0.481952:0.772282:0.465942:0.772282:0.000000:0.000000
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’( ):@0.164301:0.777579:0.187281:0.777579:0.187281:0.761846:0.164301:0.761846:0.000000:0.000000:0.000000:0.000000
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5:@0.315019:0.777579:0.323652:0.777579:0.323652:0.761846:0.315019:0.761846:0.000000
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5:@0.415431:0.777579:0.424064:0.777579:0.424064:0.761846:0.415431:0.761846:0.000000
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3:@0.293608:0.770219:0.298611:0.770219:0.298611:0.761100:0.293608:0.761100:0.000000
3:@0.394021:0.770219:0.399024:0.770219:0.399024:0.761100:0.394021:0.761100:0.000000
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x:@0.271097:0.807594:0.278262:0.807594:0.278262:0.791887:0.271097:0.791887:0.000000
x:@0.338781:0.807594:0.345946:0.807594:0.345946:0.791887:0.338781:0.791887:0.000000
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2:@0.209433:0.807593:0.218065:0.807593:0.218065:0.791860:0.209433:0.791860:0.000000
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5:@0.301211:0.807593:0.309844:0.807593:0.309844:0.791860:0.301211:0.791860:0.000000
5:@0.368913:0.807593:0.377546:0.807593:0.377546:0.791860:0.368913:0.791860:0.000000
3 2:@0.401375:0.807593:0.433182:0.807593:0.433182:0.791860:0.401375:0.791860:0.000000:0.000000:0.000000
8:@0.202657:0.832116:0.211290:0.832116:0.211290:0.816382:0.202657:0.816382:0.000000
3:@0.243009:0.832116:0.251642:0.832116:0.251642:0.816382:0.243009:0.816382:0.000000
20:@0.282512:0.832116:0.299690:0.832116:0.299690:0.816382:0.282512:0.816382:0.000000:0.000000
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2:@0.279791:0.800243:0.284794:0.800243:0.284794:0.791125:0.279791:0.791125:0.000000
3:@0.347488:0.800243:0.352491:0.800243:0.352491:0.791125:0.347488:0.791125:0.000000
3:@0.221290:0.824758:0.226294:0.824758:0.226294:0.815640:0.221290:0.815640:0.000000
2:@0.261090:0.824758:0.266094:0.824758:0.266094:0.815640:0.261090:0.815640:0.000000
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’( ):@0.164300:0.832121:0.187280:0.832121:0.187280:0.816388:0.164300:0.816388:0.000000:0.000000:0.000000:0.000000
’’()18 1:@0.164300:0.855661:0.221936:0.855661:0.221936:0.839928:0.164300:0.839928:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
’( ):@0.164300:0.876666:0.182061:0.876666:0.182061:0.860932:0.164300:0.860932:0.000000:0.000000:0.000000:0.000000
3 1:@0.247675:0.855661:0.271646:0.855661:0.271646:0.839928:0.247675:0.839928:0.000000:0.000000:0.000000
201 1:@0.297085:0.855661:0.356331:0.855661:0.356331:0.839928:0.297085:0.839928:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.171252:0.876666:0.179885:0.876666:0.179885:0.860932:0.171252:0.860932:0.000000
8:@0.207642:0.876666:0.216275:0.876666:0.216275:0.860932:0.207642:0.860932:0.000000
3:@0.225966:0.846449:0.230969:0.846449:0.230969:0.837331:0.225966:0.837331:0.000000
2:@0.275670:0.846449:0.280673:0.846449:0.280673:0.837331:0.275670:0.837331:0.000000
=:@0.184905:0.855254:0.194617:0.855254:0.194617:0.838990:0.184905:0.838990:0.000000
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  Hallamos la derivada por cociente en   = 1.:@0.577948:0.722866:0.904464:0.722866:0.904464:0.706477:0.577948:0.706477:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
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x:@0.762895:0.783593:0.769985:0.783593:0.769985:0.768868:0.762895:0.768868:0.000000
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5 52:@0.679496:0.830798:0.710728:0.830798:0.710728:0.816048:0.679496:0.816048:0.000000:0.000000:0.000000:0.000000
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) ):@0.814077:0.892821:0.819907:0.892821:0.819907:0.873334:0.814077:0.873334:0.000000:0.000000:0.000000
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2:@0.819945:0.882992:0.824896:0.882992:0.824896:0.874443:0.819945:0.874443:0.000000
1 ’( ):@0.607930:0.919202:0.618644:0.919202:0.618644:0.904452:0.607930:0.904452:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
12:@0.635240:0.911310:0.652239:0.911310:0.652239:0.896560:0.635240:0.896560:0.000000:0.000000
49:@0.635783:0.928960:0.652781:0.928960:0.652781:0.914210:0.635783:0.914210:0.000000:0.000000
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’( ) 65:@0.437808:0.655491:0.504667:0.655491:0.504667:0.639102:0.437808:0.639102:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
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=:@0.464716:0.655063:0.474832:0.655063:0.474832:0.638120:0.464716:0.638120:0.000000
−:@0.524126:0.655063:0.534243:0.655063:0.534243:0.638120:0.524126:0.638120:0.000000
5:@0.479955:0.589120:0.488948:0.589120:0.488948:0.572731:0.479955:0.572731:0.000000
2:@0.520846:0.589120:0.529839:0.589120:0.529839:0.572731:0.520846:0.572731:0.000000
1:@0.553776:0.589120:0.562769:0.589120:0.562769:0.572731:0.553776:0.572731:0.000000
2:@0.536547:0.621579:0.545539:0.621579:0.545539:0.605191:0.536547:0.605191:0.000000
1:@0.569477:0.621579:0.578469:0.621579:0.578469:0.605191:0.569477:0.605191:0.000000
5:@0.620945:0.621579:0.629938:0.621579:0.629938:0.605191:0.620945:0.605191:0.000000
2:@0.661836:0.621579:0.670829:0.621579:0.670829:0.605191:0.661836:0.605191:0.000000
1:@0.694766:0.621579:0.703759:0.621579:0.703759:0.605191:0.694766:0.605191:0.000000
3:@0.498535:0.581454:0.503747:0.581454:0.503747:0.571956:0.498535:0.571956:0.000000
6:@0.567120:0.577718:0.572332:0.577718:0.572332:0.568220:0.567120:0.568220:0.000000
3:@0.514245:0.613908:0.519457:0.613908:0.519457:0.604409:0.514245:0.604409:0.000000
5:@0.582670:0.610172:0.587881:0.610172:0.587881:0.600674:0.582670:0.600674:0.000000
3:@0.639528:0.613908:0.644740:0.613908:0.644740:0.604409:0.639528:0.604409:0.000000
3:@0.514256:0.647812:0.519468:0.647812:0.519468:0.638314:0.514256:0.638314:0.000000
2 2:@0.536542:0.655478:0.545534:0.655478:0.545534:0.639089:0.536542:0.639089:0.000000:0.000000:0.000000
1:@0.569472:0.655478:0.578464:0.655478:0.578464:0.639089:0.569472:0.639089:0.000000
15:@0.597003:0.655478:0.614896:0.655478:0.614896:0.639089:0.597003:0.639089:0.000000:0.000000
2:@0.646794:0.655478:0.655787:0.655478:0.655787:0.639089:0.646794:0.639089:0.000000
5:@0.582663:0.644082:0.587874:0.644082:0.587874:0.634584:0.582663:0.634584:0.000000
2:@0.624495:0.647817:0.629707:0.647817:0.629707:0.638319:0.624495:0.638319:0.000000
x:@0.546332:0.655478:0.553795:0.655478:0.553795:0.639116:0.546332:0.639116:0.000000
x:@0.615435:0.655478:0.622899:0.655478:0.622899:0.639116:0.615435:0.639116:0.000000
+:@0.557904:0.655063:0.568021:0.655063:0.568021:0.638120:0.557904:0.638120:0.000000
(:@0.488640:0.658450:0.494776:0.658450:0.494776:0.631833:0.488640:0.631833:0.000000
) (:@0.576484:0.658450:0.597281:0.658450:0.597281:0.631833:0.576484:0.631833:0.000000:0.000000:0.000000
−:@0.634386:0.655063:0.644502:0.655063:0.644502:0.638120:0.634386:0.638120:0.000000
):@0.656378:0.658450:0.662515:0.658450:0.662515:0.631833:0.656378:0.631833:0.000000
Derivada de la función compuesta. Regla de la cadena:@0.096359:0.496854:0.640118:0.496854:0.640118:0.475344:0.096359:0.475344:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Si   y   son dos funciones derivables, entonces la función compuesta:  ():@0.096359:0.519636:0.632498:0.519749:0.632498:0.503360:0.096359:0.503247:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f g:@0.112520:0.519636:0.142115:0.519636:0.142115:0.503275:0.112520:0.503275:0.000000:0.000000:0.000000
fx:@0.604451:0.519749:0.625790:0.519749:0.625790:0.503388:0.604451:0.503388:0.000000:0.000000
gh x:@0.649322:0.519749:0.694120:0.519749:0.694120:0.503388:0.649322:0.503388:0.000000:0.000000:0.000000:0.000000
=:@0.635464:0.519334:0.645581:0.519334:0.645581:0.502392:0.635464:0.502392:0.000000
():@0.678161:0.521084:0.702670:0.521084:0.702670:0.499432:0.678161:0.499432:0.000000:0.000000
(:@0.660258:0.522267:0.666394:0.522267:0.666394:0.497531:0.660258:0.497531:0.000000
):@0.703545:0.522267:0.709681:0.522267:0.709681:0.497531:0.703545:0.497531:0.000000
 :@0.712504:0.519636:0.716539:0.519636:0.716539:0.503247:0.712504:0.503247:0.000000
tiene por derivada:  ’( ):@0.096357:0.536233:0.273194:0.536524:0.273194:0.520135:0.096357:0.519844:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
fx:@0.240358:0.536524:0.266506:0.536524:0.266506:0.520163:0.240358:0.520163:0.000000:0.000000
gh xh x:@0.290038:0.536524:0.386544:0.536524:0.386544:0.520163:0.290038:0.520163:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
’:@0.300670:0.536524:0.303876:0.536524:0.303876:0.520135:0.300670:0.520135:0.000000
’:@0.366309:0.536524:0.369515:0.536524:0.369515:0.520135:0.366309:0.520135:0.000000
=:@0.276161:0.536109:0.286278:0.536109:0.286278:0.519167:0.276161:0.519167:0.000000
() ():@0.322863:0.537859:0.395116:0.537859:0.395116:0.516207:0.322863:0.516207:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.304958:0.539042:0.311095:0.539042:0.311095:0.514306:0.304958:0.514306:0.000000
):@0.348245:0.539042:0.354381:0.539042:0.354381:0.514306:0.348245:0.514306:0.000000
1.:@0.096359:0.563521:0.110585:0.563521:0.110585:0.546620:0.096359:0.546620:0.000000:0.000000
  Hallamos la derivada de las siguientes funciones compuestas.:@0.110585:0.563521:0.574330:0.563521:0.574330:0.547132:0.110585:0.547132:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2.:@0.096359:0.701741:0.110585:0.701741:0.110585:0.684841:0.096359:0.684841:0.000000:0.000000
  Encontramos la derivada en un punto.:@0.110585:0.701741:0.404963:0.701741:0.404963:0.685352:0.110585:0.685352:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
nidad de conocimientos:@0.117728:0.465727:0.291399:0.465727:0.291399:0.450363:0.117728:0.450363:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
U:@0.095893:0.466511:0.108460:0.466511:0.108460:0.449376:0.095893:0.449376:0.000000
Los agricultores ofrecen :@0.754293:0.246646:0.916622:0.246646:0.916622:0.231747:0.754293:0.231747:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sus productos a precios :@0.754293:0.261734:0.915047:0.261734:0.915047:0.246835:0.754293:0.246835:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
justos, evitando la :@0.754293:0.276821:0.877203:0.276821:0.877203:0.261922:0.754293:0.261922:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
especulación. Sin :@0.754293:0.291909:0.872933:0.291909:0.872933:0.277010:0.754293:0.277010:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
embargo, muchos :@0.754293:0.306996:0.879986:0.306996:0.879986:0.292097:0.754293:0.292097:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
insisten en regatear, :@0.754293:0.322084:0.890572:0.322084:0.890572:0.307185:0.754293:0.307185:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
olvidando el esfuerzo :@0.754293:0.337172:0.900655:0.337172:0.900655:0.322273:0.754293:0.322273:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
detrás de cada cosecha. :@0.754293:0.352259:0.916942:0.352259:0.916942:0.337360:0.754293:0.337360:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Reflexiona: ¿somos éticos :@0.754293:0.471816:0.916086:0.471816:0.916086:0.456942:0.754293:0.456942:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y justos al comprar?:@0.754293:0.485646:0.879113:0.485646:0.879113:0.470772:0.754293:0.470772:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
   Ética e integridad:@0.769375:0.214204:0.912226:0.214204:0.912226:0.197303:0.769375:0.197303:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
©Shutterstock:@0.947692:0.444652:0.947692:0.401827:0.935781:0.401827:0.935781:0.444652:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Paso 1. :@0.104446:0.095119:0.160081:0.095119:0.160081:0.079541:0.104446:0.079541:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Calculamos la derivada de la :@0.160081:0.095119:0.352713:0.095119:0.352713:0.080220:0.160081:0.080220:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
función del costo total  ( ), para ello :@0.104446:0.110206:0.350118:0.110206:0.350118:0.095307:0.104446:0.095307:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C x:@0.257980:0.110206:0.278217:0.110206:0.278217:0.095332:0.257980:0.095332:0.000000:0.000000:0.000000
aplicamos las reglas de derivación.:@0.104446:0.125294:0.333783:0.125294:0.333783:0.110395:0.104446:0.110395:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.104446:0.217617:0.108115:0.217617:0.108115:0.202718:0.104446:0.202718:0.000000
Cx:@0.110376:0.146946:0.132932:0.146946:0.132932:0.132221:0.110376:0.132221:0.000000:0.000000
x:@0.174593:0.146946:0.181310:0.146946:0.181310:0.132221:0.174593:0.132221:0.000000
x:@0.211627:0.146946:0.218344:0.146946:0.218344:0.132221:0.211627:0.132221:0.000000
x:@0.256439:0.146946:0.263156:0.146946:0.263156:0.132221:0.256439:0.132221:0.000000
Cx:@0.110376:0.173503:0.137260:0.173503:0.137260:0.158777:0.110376:0.158777:0.000000:0.000000
d:@0.162718:0.165611:0.171060:0.165611:0.171060:0.150886:0.162718:0.150886:0.000000
dx:@0.159235:0.183261:0.174245:0.183261:0.174245:0.168536:0.159235:0.168536:0.000000:0.000000
x:@0.205739:0.173503:0.212456:0.173503:0.212456:0.158777:0.205739:0.158777:0.000000
x:@0.242773:0.173503:0.249490:0.173503:0.249490:0.158777:0.242773:0.158777:0.000000
x:@0.287586:0.173503:0.294302:0.173503:0.294302:0.158777:0.287586:0.158777:0.000000
Cx:@0.110376:0.206886:0.137260:0.206886:0.137260:0.192161:0.110376:0.192161:0.000000:0.000000
() 05:@0.120223:0.146946:0.174110:0.146946:0.174110:0.132196:0.120223:0.132196:0.000000:0.000000:0.000000:0.000000:0.000000
,:@0.161635:0.146946:0.164521:0.146946:0.164521:0.132196:0.161635:0.132196:0.000000
’( ):@0.121730:0.173503:0.143274:0.173503:0.143274:0.158752:0.121730:0.158752:0.000000:0.000000:0.000000:0.000000
, 05:@0.192780:0.173503:0.205254:0.173503:0.205254:0.158752:0.192780:0.158752:0.000000:0.000000:0.000000:0.000000
’( ):@0.121730:0.206886:0.143274:0.206886:0.143274:0.192136:0.121730:0.192136:0.000000:0.000000:0.000000:0.000000
=:@0.141614:0.146572:0.150719:0.146572:0.150719:0.131324:0.141614:0.131324:0.000000
−:@0.191650:0.146572:0.200756:0.146572:0.200756:0.131324:0.191650:0.131324:0.000000
+:@0.228684:0.146572:0.237790:0.146572:0.237790:0.131324:0.228684:0.131324:0.000000
+:@0.266846:0.146572:0.275951:0.146572:0.275951:0.131324:0.266846:0.131324:0.000000
=:@0.145949:0.173129:0.155054:0.173129:0.155054:0.157881:0.145949:0.157881:0.000000
−:@0.222804:0.173129:0.231909:0.173129:0.231909:0.157881:0.222804:0.157881:0.000000
+:@0.259821:0.173129:0.268926:0.173129:0.268926:0.157881:0.259821:0.157881:0.000000
+:@0.297983:0.173129:0.307088:0.173129:0.307088:0.157881:0.297983:0.157881:0.000000
(:@0.178176:0.176178:0.183699:0.176178:0.183699:0.152223:0.178176:0.152223:0.000000
):@0.333560:0.176178:0.339082:0.176178:0.339082:0.152223:0.333560:0.152223:0.000000
=:@0.145949:0.206510:0.155054:0.206510:0.155054:0.191263:0.145949:0.191263:0.000000
3:@0.202818:0.146946:0.210912:0.146946:0.210912:0.132196:0.202818:0.132196:0.000000
10:@0.239106:0.146946:0.255193:0.146946:0.255193:0.132196:0.239106:0.132196:0.000000:0.000000
100:@0.277251:0.146946:0.301366:0.146946:0.301366:0.132196:0.277251:0.132196:0.000000:0.000000:0.000000
3:@0.233963:0.173503:0.242056:0.173503:0.242056:0.158752:0.233963:0.158752:0.000000
10:@0.270250:0.173503:0.286338:0.173503:0.286338:0.158752:0.270250:0.158752:0.000000:0.000000
100:@0.308396:0.173503:0.332510:0.173503:0.332510:0.158752:0.308396:0.158752:0.000000:0.000000:0.000000
3:@0.158982:0.198995:0.167076:0.198995:0.167076:0.184245:0.158982:0.184245:0.000000
2:@0.159000:0.216644:0.167093:0.216644:0.167093:0.201894:0.159000:0.201894:0.000000
3:@0.182746:0.140051:0.187437:0.140051:0.187437:0.131503:0.182746:0.131503:0.000000
2:@0.219780:0.140051:0.224470:0.140051:0.224470:0.131503:0.219780:0.131503:0.000000
3:@0.213890:0.166607:0.218581:0.166607:0.218581:0.158058:0.213890:0.158058:0.000000
2:@0.250924:0.166607:0.255615:0.166607:0.255615:0.158058:0.250924:0.158058:0.000000
x x:@0.170637:0.206884:0.177354:0.206884:0.177354:0.192159:0.170637:0.192159:0.000000:0.000000:0.000000
x:@0.208418:0.206884:0.215135:0.206884:0.215135:0.192159:0.208418:0.192159:0.000000
2:@0.178789:0.199988:0.183480:0.199988:0.183480:0.191440:0.178789:0.191440:0.000000
6:@0.199096:0.206884:0.207190:0.206884:0.207190:0.192134:0.199096:0.192134:0.000000
10:@0.229248:0.206884:0.245352:0.206884:0.245352:0.192134:0.229248:0.192134:0.000000:0.000000
−:@0.187686:0.206510:0.196791:0.206510:0.196791:0.191263:0.187686:0.191263:0.000000
+:@0.218832:0.206510:0.227937:0.206510:0.227937:0.191263:0.218832:0.191263:0.000000
A la derivada de la función de costo total se :@0.104446:0.236272:0.397859:0.236272:0.397859:0.221373:0.104446:0.221373:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
le conoce como costo marginal.:@0.104446:0.251360:0.317769:0.251360:0.317769:0.236461:0.104446:0.236461:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Paso 2. :@0.405922:0.095115:0.461557:0.095115:0.461557:0.079537:0.405922:0.079537:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Evaluamos en la derivada cuánto :@0.461557:0.095115:0.684643:0.095115:0.684643:0.080216:0.461557:0.080216:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cuesta producir un saco más, por ejemplo::@0.405922:0.110202:0.687995:0.110202:0.687995:0.095303:0.405922:0.095303:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Si   = 4 (400 sacos):@0.405922:0.132419:0.530376:0.132419:0.530376:0.117520:0.405922:0.117520:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.420865:0.132419:0.427650:0.132419:0.427650:0.117545:0.420865:0.117545:0.000000
C:@0.408186:0.160071:0.417109:0.160071:0.417109:0.145346:0.408186:0.145346:0.000000
’( ):@0.419547:0.160071:0.440577:0.160071:0.440577:0.145321:0.419547:0.145321:0.000000:0.000000:0.000000:0.000000
4:@0.427607:0.160071:0.435701:0.160071:0.435701:0.145321:0.427607:0.145321:0.000000
3:@0.456293:0.152185:0.464386:0.152185:0.464386:0.137435:0.456293:0.137435:0.000000
2:@0.456293:0.169835:0.464386:0.169835:0.464386:0.155085:0.456293:0.155085:0.000000
4:@0.473537:0.160071:0.481631:0.160071:0.481631:0.145321:0.473537:0.145321:0.000000
6 4:@0.508548:0.160071:0.533077:0.160071:0.533077:0.145321:0.508548:0.145321:0.000000:0.000000:0.000000
1024241010:@0.552365:0.160071:0.688235:0.160071:0.688235:0.145321:0.552365:0.145321:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.488238:0.151442:0.492928:0.151442:0.492928:0.142894:0.488238:0.142894:0.000000
=:@0.443241:0.159697:0.452346:0.159697:0.452346:0.144449:0.443241:0.144449:0.000000
():@0.466659:0.161272:0.488203:0.161272:0.488203:0.141785:0.466659:0.141785:0.000000:0.000000
−:@0.497142:0.159697:0.506247:0.159697:0.506247:0.144449:0.497142:0.144449:0.000000
():@0.518109:0.161272:0.539653:0.161272:0.539653:0.141785:0.518109:0.141785:0.000000:0.000000
+:@0.541949:0.159697:0.551054:0.159697:0.551054:0.144449:0.541949:0.144449:0.000000
=:@0.571586:0.159697:0.580692:0.159697:0.580692:0.144449:0.571586:0.144449:0.000000
−:@0.601970:0.159697:0.611075:0.159697:0.611075:0.144449:0.601970:0.144449:0.000000
+:@0.631790:0.159697:0.640895:0.159697:0.640895:0.144449:0.631790:0.144449:0.000000
=:@0.661427:0.159697:0.670532:0.159697:0.670532:0.144449:0.661427:0.144449:0.000000
Producir un saco adicional cuando ya se :@0.405925:0.189228:0.675940:0.189228:0.675940:0.174329:0.405925:0.174329:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tienen 400 cuesta $10 más.:@0.405925:0.204315:0.586362:0.204315:0.586362:0.189416:0.405925:0.189416:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000