135:@0.937671:0.974518:0.968375:0.974518:0.968375:0.956333:0.937671:0.956333:0.000000:0.000000:0.000000
Pensamiento numérico y variacional:@0.603971:0.043660:0.926928:0.043660:0.926928:0.024915:0.603971:0.024915:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Tal como lo veremos en el Ejemplo 8, cuando aplicamos la regla de la cadena a una :@0.073089:0.136836:0.710070:0.136836:0.710070:0.120402:0.073089:0.120402:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
función compuesta es necesario volver a aplicar dicha regla para calcular la derivada :@0.073089:0.153478:0.710431:0.153478:0.710431:0.137044:0.073089:0.137044:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
interna, es decir, se debe aplicar la regla de la cadena por segunda vez.:@0.073089:0.170120:0.582594:0.170120:0.582594:0.153686:0.073089:0.153686:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejemplo 4. :@0.073089:0.201753:0.156437:0.201753:0.156437:0.185084:0.073089:0.185084:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Determina :@0.156308:0.201753:0.237812:0.201753:0.237812:0.185319:0.156308:0.185319:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dy:@0.243686:0.194016:0.260345:0.194016:0.260345:0.177610:0.243686:0.177610:0.000000:0.000000
dx:@0.243705:0.210408:0.260345:0.210408:0.260345:0.194002:0.243705:0.194002:0.000000:0.000000
sabiendo que :@0.266272:0.201755:0.369960:0.201755:0.369960:0.185321:0.266272:0.185321:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y = sen cos x:@0.369794:0.201755:0.479948:0.201748:0.479948:0.185342:0.369794:0.185348:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.418046:0.195684:0.423283:0.195684:0.423283:0.186103:0.418046:0.186103:0.000000
 (:@0.423235:0.201748:0.432071:0.201748:0.432071:0.185314:0.423235:0.185314:0.000000:0.000000
 (2 )). :@0.454841:0.201748:0.496717:0.201748:0.496717:0.185314:0.454841:0.185314:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Solución: :@0.073074:0.241924:0.143456:0.241924:0.143456:0.225491:0.073074:0.225491:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
                         = 5[:@0.073089:0.273554:0.200670:0.273554:0.200670:0.257120:0.073089:0.257120:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sen cos cos x:@0.200391:0.273554:0.302735:0.273554:0.302735:0.257148:0.200391:0.257148:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.223841:0.273554:0.228719:0.273554:0.228719:0.257120:0.223841:0.257120:0.000000
 (2 )]  [–:@0.277627:0.273554:0.335408:0.273554:0.335408:0.257120:0.277627:0.257120:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4:@0.312251:0.267490:0.317488:0.267490:0.317488:0.257909:0.312251:0.257909:0.000000
sen x:@0.335316:0.273554:0.379917:0.273554:0.379917:0.257148:0.335316:0.257148:0.000000:0.000000:0.000000:0.000000:0.000000
(2 ) :@0.358767:0.273554:0.388678:0.273554:0.388678:0.257120:0.358767:0.257120:0.000000:0.000000:0.000000:0.000000:0.000000
(d(2x)):@0.397402:0.265823:0.441439:0.265823:0.441439:0.249417:0.397402:0.249417:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.415717:0.282215:0.423172:0.282215:0.423172:0.265809:0.415717:0.265809:0.000000
                         = [5:@0.073103:0.297345:0.200683:0.297345:0.200683:0.280912:0.073103:0.280912:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sen cos cos  x:@0.200407:0.297345:0.311149:0.297344:0.311149:0.280938:0.200407:0.280939:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4:@0.223845:0.291280:0.229082:0.291280:0.229082:0.281699:0.223845:0.281699:0.000000
 (:@0.229034:0.297344:0.237869:0.297344:0.237869:0.280910:0.229034:0.280910:0.000000:0.000000
(2 )][–:@0.289999:0.297344:0.334692:0.297344:0.334692:0.280910:0.289999:0.280910:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sen x:@0.334581:0.297344:0.379182:0.297344:0.379182:0.280938:0.334581:0.280938:0.000000:0.000000:0.000000:0.000000:0.000000
(2 ) × 2]:@0.358032:0.297344:0.416512:0.297344:0.416512:0.280910:0.358032:0.280910:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
                         = – 2[:@0.073051:0.321128:0.213719:0.321128:0.213719:0.304694:0.073051:0.304694:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sen cos cos  x sen x:@0.213425:0.321128:0.382298:0.321133:0.382298:0.304727:0.213425:0.304722:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4:@0.236917:0.315069:0.242154:0.315069:0.242154:0.305488:0.236917:0.305488:0.000000
 (:@0.242108:0.321133:0.250944:0.321133:0.250944:0.304699:0.242108:0.304699:0.000000:0.000000
(2 )] :@0.303073:0.321133:0.337789:0.321133:0.337789:0.304699:0.303073:0.304699:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(2 ).:@0.361148:0.321133:0.390231:0.321133:0.390231:0.304699:0.361148:0.304699:0.000000:0.000000:0.000000:0.000000:0.000000
Ejemplo 5.:@0.073056:0.348495:0.152594:0.348495:0.152594:0.331826:0.073056:0.331826:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Una partícula material se mueve sobre un eje de coordenadas. Su posición :@0.152483:0.348495:0.700456:0.348495:0.700456:0.332061:0.152483:0.332061:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
s :@0.699952:0.348495:0.709634:0.348495:0.709634:0.332089:0.699952:0.332089:0.000000:0.000000
en el tiempo  viene dada por  ( ) = :@0.073074:0.365137:0.340587:0.365137:0.340587:0.348703:0.073074:0.348703:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t :@0.172934:0.365137:0.181659:0.365137:0.181659:0.348731:0.172934:0.348731:0.000000:0.000000
s t:@0.299097:0.365137:0.315811:0.365137:0.315811:0.348731:0.299097:0.348731:0.000000:0.000000:0.000000
sen t:@0.341286:0.365137:0.384415:0.365137:0.384415:0.348731:0.341286:0.348731:0.000000:0.000000:0.000000:0.000000:0.000000
(3 ) + :@0.365069:0.365137:0.409191:0.365137:0.409191:0.348703:0.365069:0.348703:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cos t:@0.409890:0.365137:0.452429:0.365137:0.452429:0.348731:0.409890:0.348731:0.000000:0.000000:0.000000:0.000000:0.000000
(2 ). ¿Con qué velocidad se mueve la :@0.433083:0.365137:0.710499:0.365137:0.710499:0.348703:0.433083:0.348703:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
partícula en el instante   = :@0.073093:0.386050:0.266203:0.386050:0.266203:0.369616:0.073093:0.369616:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.242016:0.386050:0.247391:0.386050:0.247391:0.369644:0.242016:0.369644:0.000000
π:@0.272204:0.378313:0.281408:0.378313:0.281408:0.361907:0.272204:0.361907:0.000000
6:@0.272314:0.394705:0.281297:0.394705:0.281297:0.378271:0.272314:0.378271:0.000000
 ?:@0.287408:0.386051:0.298379:0.386051:0.298379:0.369618:0.287408:0.369618:0.000000:0.000000
Solución::@0.073093:0.413413:0.139517:0.413413:0.139517:0.396980:0.073093:0.396980:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La velocidad  ( ) con la que se mueve la partícula en un instante  está dada por  ´( ).:@0.073093:0.433633:0.681710:0.433633:0.681710:0.417199:0.073093:0.417199:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v t:@0.167964:0.433633:0.185800:0.433633:0.185800:0.417227:0.167964:0.417227:0.000000:0.000000:0.000000
t :@0.540379:0.433633:0.548994:0.433633:0.548994:0.417227:0.540379:0.417227:0.000000:0.000000
s t:@0.651872:0.433633:0.673777:0.433633:0.673777:0.417227:0.651872:0.417227:0.000000:0.000000:0.000000
v t:@0.279475:0.457417:0.297311:0.457417:0.297311:0.441011:0.279475:0.441011:0.000000:0.000000:0.000000
( ) =  '( ) = 3:@0.287132:0.457417:0.373002:0.457417:0.373002:0.440983:0.287132:0.440983:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
s t:@0.320818:0.457417:0.340476:0.457417:0.340476:0.441011:0.320818:0.441011:0.000000:0.000000:0.000000
cos t:@0.372892:0.457417:0.418781:0.457417:0.418781:0.441011:0.372892:0.441011:0.000000:0.000000:0.000000:0.000000:0.000000
 (3 ) – 2:@0.395753:0.457417:0.449539:0.457417:0.449539:0.440983:0.395753:0.440983:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sen t:@0.449429:0.457417:0.491950:0.457417:0.491950:0.441011:0.449429:0.441011:0.000000:0.000000:0.000000:0.000000:0.000000
(2 ).:@0.472880:0.457417:0.499883:0.457417:0.499883:0.440983:0.472880:0.440983:0.000000:0.000000:0.000000:0.000000:0.000000
Como se pregunta la velocidad en el instante   = :@0.073019:0.489938:0.419260:0.489938:0.419260:0.473504:0.073019:0.473504:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.395717:0.489938:0.401092:0.489938:0.401092:0.473532:0.395717:0.473532:0.000000
π:@0.425078:0.481308:0.434282:0.481308:0.434282:0.464902:0.425078:0.464902:0.000000
6:@0.425188:0.497701:0.434171:0.497701:0.434171:0.481267:0.425188:0.481267:0.000000
, debemos reemplazar   por :@0.440098:0.489934:0.638584:0.489934:0.638584:0.473501:0.440098:0.473501:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
t:@0.601143:0.489934:0.606518:0.489934:0.606518:0.473528:0.601143:0.473528:0.000000
π:@0.644328:0.481308:0.653532:0.481308:0.653532:0.464902:0.644328:0.464902:0.000000
6:@0.644439:0.497701:0.653422:0.497701:0.653422:0.481267:0.644439:0.481267:0.000000
en  ( ).:@0.659349:0.489934:0.706342:0.489934:0.706342:0.473501:0.659349:0.473501:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v t:@0.681309:0.489934:0.698777:0.489934:0.698777:0.473528:0.681309:0.473528:0.000000:0.000000:0.000000
.:@0.693727:0.522928:0.696930:0.522928:0.696930:0.506494:0.693727:0.506494:0.000000
Ejemplo 6. :@0.073089:0.557438:0.156621:0.557438:0.156621:0.540769:0.073089:0.540769:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El número de euros del costo total de producir x unidades de cierto artículo :@0.156713:0.557438:0.710836:0.557438:0.710836:0.541005:0.156713:0.541005:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
está dado por :@0.073089:0.574080:0.186662:0.574080:0.186662:0.557646:0.073089:0.557646:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Determina: a) el costo marginal cuando se :@0.363594:0.574080:0.710273:0.574080:0.710273:0.557646:0.363594:0.557646:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
producen 50 unidades; b) el número de unidades producidas cuando el costo marginal :@0.073089:0.590722:0.710750:0.590722:0.710750:0.574288:0.073089:0.574288:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
es de 4,5 euros.:@0.073089:0.607364:0.183557:0.607364:0.183557:0.590930:0.073089:0.590930:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Solución:@0.073089:0.634727:0.136384:0.634727:0.136384:0.618293:0.073089:0.618293:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.136336:0.634727:0.140367:0.634727:0.140367:0.618293:0.136336:0.618293:0.000000
a.  Para hallar el costo marginal, derivamos el costo total con respecto a x.:@0.104633:0.654943:0.643439:0.654943:0.643439:0.638509:0.104633:0.638509:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Como   = 50 unidades, entonces :@0.134754:0.711132:0.376888:0.711132:0.376888:0.694698:0.134754:0.694698:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.183424:0.711132:0.190879:0.711132:0.190879:0.694726:0.183424:0.694726:0.000000
.:@0.473959:0.733722:0.477162:0.733722:0.477162:0.717288:0.473959:0.717288:0.000000
Por lo tanto, el costo marginal cuando se producen 50 unidades es de 3,9 euros.:@0.134754:0.764660:0.706823:0.764660:0.706823:0.748226:0.134754:0.748226:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b.  Para determinar el número de unidades cuando el costo marginal es de 4,5 :@0.104633:0.792021:0.710576:0.792021:0.710576:0.775588:0.104633:0.775588:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
euros, utilizamos la función de costo marginal en la que reemplazamos   ( ) :@0.134760:0.808663:0.710369:0.808663:0.710369:0.792229:0.134760:0.792229:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C x:@0.667043:0.808663:0.701423:0.808663:0.701423:0.792257:0.667043:0.792257:0.000000:0.000000:0.000000
m:@0.676981:0.808409:0.684340:0.808409:0.684340:0.800149:0.676981:0.800149:0.000000
por 4,5 y, luego, despejamos la variable  .:@0.134755:0.825305:0.431370:0.825305:0.431370:0.808871:0.134755:0.808871:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.420786:0.825305:0.428241:0.825305:0.428241:0.808899:0.420786:0.808899:0.000000
Supongamos que el :@0.740548:0.298654:0.877515:0.298654:0.877515:0.283714:0.740548:0.283714:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
bienestar emocional de :@0.740548:0.312522:0.899938:0.312522:0.899938:0.297582:0.740548:0.297582:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
una persona depende :@0.740548:0.326390:0.890550:0.326390:0.890550:0.311451:0.740548:0.311451:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de sus niveles de estrés, :@0.740548:0.340259:0.900353:0.340259:0.900353:0.325319:0.740548:0.325319:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y que estos niveles de :@0.740548:0.354127:0.888616:0.354127:0.888616:0.339187:0.740548:0.339187:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
estrés están influidos por la :@0.740548:0.367995:0.922974:0.367995:0.922974:0.353055:0.740548:0.353055:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cantidad de ejercicio físico :@0.740548:0.381863:0.918489:0.381863:0.918489:0.366923:0.740548:0.366923:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
diario. ¿Cómo podríamos :@0.740548:0.395731:0.909866:0.395731:0.909866:0.380792:0.740548:0.380792:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
expresar el cambio en el :@0.740548:0.409600:0.904316:0.409600:0.904316:0.394660:0.740548:0.394660:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
bienestar emocional en :@0.740548:0.423468:0.899804:0.423468:0.899804:0.408528:0.740548:0.408528:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
función del cambio en el :@0.740548:0.437336:0.908320:0.437336:0.908320:0.422396:0.740548:0.422396:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ejercicio físico?:@0.740548:0.451204:0.838886:0.451204:0.838886:0.436264:0.740548:0.436264:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Aquí, la regla de la cadena :@0.740548:0.468640:0.916240:0.468640:0.916240:0.453701:0.740548:0.453701:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
nos ayuda a ver cómo un :@0.740548:0.482509:0.910536:0.482509:0.910536:0.467569:0.740548:0.467569:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cambio en el ejercicio físico :@0.740548:0.496377:0.925519:0.496377:0.925519:0.481437:0.740548:0.481437:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
afecta indirectamente :@0.740548:0.510245:0.889096:0.510245:0.889096:0.495305:0.740548:0.495305:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el bienestar emocional :@0.740548:0.524113:0.894383:0.524113:0.894383:0.509173:0.740548:0.509173:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a través de los niveles :@0.740548:0.537981:0.886231:0.537981:0.886231:0.523042:0.740548:0.523042:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de estrés. Expresado en :@0.740548:0.551850:0.898315:0.551850:0.898315:0.536910:0.740548:0.536910:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
términos de derivadas, se :@0.740548:0.565718:0.911307:0.565718:0.911307:0.550778:0.740548:0.550778:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
vería así::@0.740548:0.579586:0.795556:0.579586:0.795556:0.564646:0.740548:0.564646:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d bienestar:@0.746924:0.602660:0.810584:0.602660:0.810584:0.589237:0.746924:0.589237:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.754439:0.602660:0.758430:0.602660:0.758430:0.589214:0.754439:0.589214:0.000000
):@0.810584:0.602660:0.814575:0.602660:0.814575:0.589214:0.810584:0.589214:0.000000
d ejercicio:@0.750192:0.615141:0.807337:0.615141:0.807337:0.601718:0.750192:0.601718:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.757707:0.615141:0.761698:0.615141:0.761698:0.601696:0.757707:0.601696:0.000000
):@0.807331:0.615141:0.811322:0.615141:0.811322:0.601696:0.807331:0.601696:0.000000
=:@0.820872:0.607329:0.830846:0.607329:0.830846:0.592389:0.820872:0.592389:0.000000
d bienestar:@0.746924:0.633504:0.810584:0.633504:0.810584:0.620081:0.746924:0.620081:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.754439:0.633504:0.758430:0.633504:0.758430:0.620058:0.754439:0.620058:0.000000
):@0.810584:0.633504:0.814575:0.633504:0.814575:0.620058:0.810584:0.620058:0.000000
d estrés:@0.757315:0.645986:0.800229:0.645986:0.800229:0.632562:0.757315:0.632562:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.764831:0.645986:0.768822:0.645986:0.768822:0.632540:0.764831:0.632540:0.000000
):@0.800193:0.645986:0.804184:0.645986:0.804184:0.632540:0.800193:0.632540:0.000000
×:@0.820872:0.639065:0.830846:0.639065:0.830846:0.624126:0.820872:0.624126:0.000000
d estrés:@0.847534:0.634397:0.890448:0.634397:0.890448:0.620974:0.847534:0.620974:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.855050:0.634397:0.859041:0.634397:0.859041:0.620951:0.855050:0.620951:0.000000
):@0.890412:0.634397:0.894403:0.634397:0.894403:0.620951:0.890412:0.620951:0.000000
d ejercicio:@0.840411:0.646878:0.897556:0.646878:0.897556:0.633455:0.840411:0.633455:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.847926:0.646878:0.851917:0.646878:0.851917:0.633432:0.847926:0.633432:0.000000
):@0.897550:0.646878:0.901541:0.646878:0.901541:0.633432:0.897550:0.633432:0.000000
Esto te permite ver cómo :@0.740548:0.667229:0.910768:0.667229:0.910768:0.652289:0.740548:0.652289:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
un hábito saludable como :@0.740548:0.681097:0.917636:0.681097:0.917636:0.666157:0.740548:0.666157:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el ejercicio, tiene efectos en :@0.740548:0.694966:0.925747:0.694966:0.925747:0.680026:0.740548:0.680026:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cadena sobre el bienestar :@0.740548:0.708834:0.913235:0.708834:0.913235:0.693894:0.740548:0.693894:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
general.:@0.740548:0.722702:0.793186:0.722702:0.793186:0.707762:0.740548:0.707762:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Cátedra :@0.740294:0.246858:0.799873:0.246858:0.799873:0.231451:0.740294:0.231451:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de salud y :@0.740294:0.261987:0.815830:0.261987:0.815830:0.246580:0.740294:0.246580:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
bienestar:@0.740294:0.277116:0.807982:0.277116:0.807982:0.261709:0.740294:0.261709:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000