122:@0.031627:0.974518:0.062330:0.974518:0.062330:0.956333:0.031627:0.956333:0.000000:0.000000:0.000000 Derivadas:@0.073089:0.043661:0.163191:0.043661:0.163191:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Ejercicios resueltos:@0.293660:0.137730:0.436670:0.137730:0.436670:0.121061:0.293660:0.121061:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Al calcular la derivada de las siguientes funciones, y al aplicar trabajo algebraico previo :@0.293660:0.172234:0.930831:0.172234:0.930831:0.155800:0.293660:0.155800:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 si es necesario, se expresa la respuesta en la misma forma en que está presentada :@0.293660:0.188876:0.930938:0.188876:0.930938:0.172442:0.293660:0.172442:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la función.:@0.293660:0.205518:0.370437:0.205518:0.370437:0.189084:0.293660:0.189084:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 • :@0.293660:0.244726:0.301318:0.244726:0.301318:0.228320:0.293660:0.228320:0.000000:0.000000 f x:@0.323846:0.244726:0.343984:0.244726:0.343984:0.228320:0.323846:0.228320:0.000000:0.000000:0.000000:0.000000 ( ) = :@0.331725:0.244726:0.387197:0.244726:0.387197:0.228292:0.331725:0.228292:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x:@0.466019:0.244726:0.489341:0.244726:0.489341:0.228320:0.466019:0.228320:0.000000:0.000000:0.000000:0.000000 '( ) = 0:@0.473897:0.244726:0.521867:0.244726:0.521867:0.228292:0.473897:0.228292:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 • :@0.293660:0.286383:0.301318:0.286383:0.301318:0.269977:0.293660:0.269977:0.000000:0.000000 f x:@0.323846:0.286383:0.343984:0.286383:0.343984:0.269977:0.323846:0.269977:0.000000:0.000000:0.000000:0.000000 ( ) = 5 :@0.331725:0.286383:0.393007:0.286383:0.393007:0.269949:0.331725:0.269949:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.376399:0.286383:0.383854:0.286383:0.383854:0.269977:0.376399:0.269977:0.000000 4:@0.383787:0.280319:0.389024:0.280319:0.389024:0.270738:0.383787:0.270738:0.000000 f x:@0.466019:0.286383:0.489341:0.286383:0.489341:0.269977:0.466019:0.269977:0.000000:0.000000:0.000000:0.000000 '( ) = 20:@0.473897:0.286383:0.530776:0.286383:0.530776:0.269949:0.473897:0.269949:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.530665:0.286383:0.538120:0.286383:0.538120:0.269977:0.530665:0.269977:0.000000 3:@0.538057:0.280319:0.543293:0.280319:0.543293:0.270738:0.538057:0.270738:0.000000 • :@0.293660:0.328042:0.301318:0.328042:0.301318:0.311636:0.293660:0.311636:0.000000:0.000000 f x:@0.323846:0.328042:0.343984:0.328042:0.343984:0.311636:0.323846:0.311636:0.000000:0.000000:0.000000:0.000000 ( ) = 7 +9 :@0.331725:0.328042:0.412814:0.328042:0.412814:0.311608:0.331725:0.311608:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.376399:0.328042:0.383854:0.328042:0.383854:0.311636:0.376399:0.311636:0.000000 6:@0.383787:0.321978:0.389024:0.321978:0.389024:0.312397:0.383787:0.312397:0.000000 f x:@0.466019:0.328042:0.489341:0.328042:0.489341:0.311636:0.466019:0.311636:0.000000:0.000000:0.000000:0.000000 '( ) = 42:@0.473897:0.328042:0.530776:0.328042:0.530776:0.311608:0.473897:0.311608:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.530665:0.328042:0.538120:0.328042:0.538120:0.311636:0.530665:0.311636:0.000000 5:@0.538057:0.321978:0.543293:0.321978:0.543293:0.312397:0.538057:0.312397:0.000000 • :@0.293660:0.374203:0.301318:0.374203:0.301318:0.357797:0.293660:0.357797:0.000000:0.000000 f x:@0.323846:0.374203:0.343984:0.374203:0.343984:0.357797:0.323846:0.357797:0.000000:0.000000:0.000000:0.000000 ( )= :@0.331725:0.374203:0.363643:0.374203:0.363643:0.357769:0.331725:0.357769:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.393923:0.374203:0.397954:0.374203:0.397954:0.357769:0.393923:0.357769:0.000000 f x:@0.466019:0.374203:0.486156:0.374203:0.486156:0.357797:0.466019:0.357797:0.000000:0.000000:0.000000:0.000000 ( ) = :@0.473897:0.374203:0.549042:0.374203:0.549042:0.357769:0.473897:0.357769:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.529281:0.374203:0.536736:0.374203:0.536736:0.357797:0.529281:0.357797:0.000000 -8:@0.536669:0.368139:0.545061:0.368139:0.545061:0.358558:0.536669:0.358558:0.000000:0.000000 f x:@0.611604:0.374203:0.634926:0.374203:0.634926:0.357797:0.611604:0.357797:0.000000:0.000000:0.000000:0.000000 '( ) = :@0.619482:0.374203:0.658542:0.374203:0.658542:0.357769:0.619482:0.357769:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 • :@0.293660:0.420408:0.301318:0.420408:0.301318:0.404002:0.293660:0.404002:0.000000:0.000000 f x:@0.323846:0.420408:0.343984:0.420408:0.343984:0.404002:0.323846:0.404002:0.000000:0.000000:0.000000:0.000000 ( )= :@0.331725:0.420408:0.363643:0.420408:0.363643:0.403974:0.331725:0.403974:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.401744:0.420408:0.405775:0.420408:0.405775:0.403974:0.401744:0.403974:0.000000 f x:@0.466019:0.420408:0.486156:0.420408:0.486156:0.404002:0.466019:0.404002:0.000000:0.000000:0.000000:0.000000 ( ) = :@0.473897:0.420408:0.509773:0.420408:0.509773:0.403974:0.473897:0.403974:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.509663:0.420408:0.517117:0.420408:0.517117:0.404002:0.509663:0.404002:0.000000 3/4:@0.517056:0.414344:0.530395:0.414344:0.530395:0.404779:0.517056:0.404779:0.000000:0.000000:0.000000 :@0.530366:0.420408:0.534397:0.420408:0.534397:0.403974:0.530366:0.403974:0.000000 f x:@0.611604:0.420408:0.634926:0.420408:0.634926:0.404002:0.611604:0.404002:0.000000:0.000000:0.000000:0.000000 '( ) = :@0.619482:0.420408:0.658542:0.420408:0.658542:0.403974:0.619482:0.403974:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 • :@0.293660:0.470640:0.301318:0.470640:0.301318:0.454234:0.293660:0.454234:0.000000:0.000000 f x:@0.323846:0.470640:0.343984:0.470640:0.343984:0.454234:0.323846:0.454234:0.000000:0.000000:0.000000:0.000000 ( ) = :@0.331725:0.470640:0.367600:0.470640:0.367600:0.454206:0.331725:0.454206:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.367508:0.470640:0.374963:0.470640:0.374963:0.454234:0.367508:0.454234:0.000000 3 :@0.374885:0.464576:0.382429:0.464576:0.382429:0.454995:0.374885:0.454995:0.000000:0.000000 :@0.420667:0.470640:0.424698:0.470640:0.424698:0.454206:0.420667:0.454206:0.000000 f x:@0.466019:0.470640:0.486156:0.470640:0.486156:0.454234:0.466019:0.454234:0.000000:0.000000:0.000000:0.000000 ( ) = :@0.473897:0.470640:0.551382:0.470640:0.551382:0.454206:0.473897:0.454206:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x x:@0.509681:0.470640:0.533659:0.470640:0.533659:0.454234:0.509681:0.454234:0.000000:0.000000:0.000000 3:@0.517056:0.464576:0.522292:0.464576:0.522292:0.454995:0.517056:0.454995:0.000000 f x:@0.611604:0.470640:0.631741:0.470640:0.631741:0.454234:0.611604:0.454234:0.000000:0.000000:0.000000:0.000000 ( ) = :@0.619482:0.470640:0.666678:0.470640:0.666678:0.454206:0.619482:0.454206:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.655266:0.470640:0.662721:0.470640:0.662721:0.454234:0.655266:0.454234:0.000000 f ' x:@0.323781:0.520870:0.346554:0.520870:0.346554:0.504464:0.323781:0.504464:0.000000:0.000000:0.000000:0.000000:0.000000 ( ) = :@0.334295:0.520870:0.370171:0.520870:0.370171:0.504437:0.334295:0.504437:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 • :@0.293660:0.566798:0.301318:0.566798:0.301318:0.550392:0.293660:0.550392:0.000000:0.000000 f x:@0.323846:0.566798:0.343984:0.566798:0.343984:0.550392:0.323846:0.550392:0.000000:0.000000:0.000000:0.000000 ( ) = (3:@0.331725:0.566798:0.381314:0.566798:0.381314:0.550364:0.331725:0.550364:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.381203:0.566798:0.388658:0.566798:0.388658:0.550392:0.381203:0.550392:0.000000 4 :@0.388585:0.560734:0.396129:0.560734:0.396129:0.551153:0.388585:0.551153:0.000000:0.000000 –:@0.396078:0.567381:0.405282:0.567381:0.405282:0.549726:0.396078:0.549726:0.000000 1) :@0.405190:0.566798:0.422934:0.566798:0.422934:0.550364:0.405190:0.550364:0.000000:0.000000:0.000000 f( ) = (3:@0.474383:0.566798:0.528709:0.566798:0.528709:0.550364:0.474383:0.550364:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.483924:0.566798:0.491379:0.566798:0.491379:0.550392:0.483924:0.550392:0.000000 x:@0.528599:0.566798:0.536054:0.566798:0.536054:0.550392:0.528599:0.550392:0.000000 4 :@0.535990:0.560734:0.543534:0.560734:0.543534:0.551153:0.535990:0.551153:0.000000:0.000000 –:@0.543483:0.567381:0.552687:0.567381:0.552687:0.549726:0.543483:0.549726:0.000000 1) :@0.552595:0.566798:0.574297:0.566798:0.574297:0.550364:0.552595:0.550364:0.000000:0.000000:0.000000:0.000000 x:@0.574187:0.566798:0.581642:0.566798:0.581642:0.550392:0.574187:0.550392:0.000000 1/3:@0.581585:0.560734:0.594924:0.560734:0.594924:0.551170:0.581585:0.551170:0.000000:0.000000:0.000000 • :@0.293660:0.613673:0.301318:0.613673:0.301318:0.597267:0.293660:0.597267:0.000000:0.000000 f ' x:@0.323846:0.613673:0.346616:0.613673:0.346616:0.597267:0.323846:0.597267:0.000000:0.000000:0.000000:0.000000:0.000000 ( ) = :@0.334357:0.613673:0.370233:0.613673:0.370233:0.597239:0.334357:0.597239:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.323781:0.678474:0.379261:0.678474:0.379261:0.662040:0.323781:0.662040:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 • :@0.293660:0.725647:0.301318:0.725647:0.301318:0.709241:0.293660:0.709241:0.000000:0.000000 f x:@0.323846:0.725647:0.343984:0.725647:0.343984:0.709241:0.323846:0.709241:0.000000:0.000000:0.000000:0.000000 ( ) = :@0.331725:0.725647:0.367600:0.725647:0.367600:0.709213:0.331725:0.709213:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.440302:0.725647:0.444334:0.725647:0.444334:0.709213:0.440302:0.709213:0.000000 f ' x:@0.323781:0.776007:0.346551:0.776007:0.346551:0.759601:0.323781:0.759601:0.000000:0.000000:0.000000:0.000000:0.000000 ( ) = :@0.334292:0.776007:0.370167:0.776007:0.370167:0.759574:0.334292:0.759574:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Competencia :@0.078581:0.670469:0.177272:0.670469:0.177272:0.655063:0.078581:0.655063:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 matemática :@0.078581:0.685598:0.167195:0.685598:0.167195:0.670192:0.078581:0.670192:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Una buena estrategia :@0.082576:0.712437:0.227444:0.712437:0.227444:0.697497:0.082576:0.697497:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 para derivadas de :@0.082576:0.727566:0.202953:0.727566:0.202953:0.712626:0.082576:0.712626:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 funciones algebraicas :@0.082576:0.742695:0.228930:0.742695:0.228930:0.727755:0.082576:0.727755:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 es simplificar la función :@0.082576:0.757824:0.239807:0.757824:0.239807:0.742884:0.082576:0.742884:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 antes de derivar. Esto :@0.082576:0.772953:0.225056:0.772953:0.225056:0.758013:0.082576:0.758013:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 facilita el proceso y reduce :@0.082576:0.788082:0.260914:0.788082:0.260914:0.773142:0.082576:0.773142:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 errores. Por ejemplo, si :@0.082576:0.803211:0.233679:0.803211:0.233679:0.788271:0.082576:0.788271:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tienes una fracción o raíz, :@0.082576:0.818340:0.252525:0.818340:0.252525:0.803400:0.082576:0.803400:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 intenta reescribirla como :@0.082576:0.833468:0.250492:0.833468:0.250492:0.818529:0.082576:0.818529:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 potencias o términos :@0.082576:0.848597:0.225831:0.848597:0.225831:0.833658:0.082576:0.833658:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 separados. Esto hará que :@0.082576:0.863726:0.249565:0.863726:0.249565:0.848786:0.082576:0.848786:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la regla de la potencia o :@0.082576:0.878855:0.243326:0.878855:0.243326:0.863915:0.082576:0.863915:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la regla de la cadena se :@0.082576:0.893984:0.238848:0.893984:0.238848:0.879044:0.082576:0.879044:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 apliquen de forma más :@0.082576:0.909113:0.238950:0.909113:0.238950:0.894173:0.082576:0.894173:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 precisa.:@0.082576:0.924242:0.131917:0.924242:0.131917:0.909302:0.082576:0.909302:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Supón que tienes una :@0.077860:0.191195:0.223462:0.191195:0.223462:0.176255:0.077860:0.176255:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 función ( ) que representa :@0.077860:0.206323:0.256615:0.206323:0.256615:0.191384:0.077860:0.191384:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 V t:@0.130672:0.206323:0.147808:0.206323:0.147808:0.191409:0.130672:0.191409:0.000000:0.000000:0.000000 las ventas del tiempo . Al :@0.077860:0.221452:0.245082:0.221452:0.245082:0.206513:0.077860:0.206513:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 t:@0.217554:0.221452:0.222441:0.221452:0.222441:0.206538:0.217554:0.206538:0.000000 derivar (t), obtienes la tasa :@0.077860:0.236581:0.256446:0.236581:0.256446:0.221641:0.077860:0.221641:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 V:@0.125468:0.236581:0.133751:0.236581:0.133751:0.221667:0.125468:0.221667:0.000000 de cambio de las ventas, es :@0.077860:0.251710:0.256598:0.251710:0.256598:0.236770:0.077860:0.236770:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 decir, el aumento o la :@0.077860:0.266839:0.219482:0.266839:0.219482:0.251899:0.077860:0.251899:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 disminución de las ventas :@0.077860:0.281968:0.247769:0.281968:0.247769:0.267028:0.077860:0.267028:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 en determinado momento. :@0.077860:0.297097:0.257975:0.297097:0.257975:0.282157:0.077860:0.282157:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 La tasa de cambio posee :@0.077860:0.312226:0.240965:0.312226:0.240965:0.297286:0.077860:0.297286:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 dos propósitos principales::@0.077860:0.327355:0.249682:0.327355:0.249682:0.312415:0.077860:0.312415:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 • Identificar tendencias de :@0.077860:0.342484:0.259070:0.342484:0.259070:0.327544:0.077860:0.327544:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 crecimiento o :@0.096840:0.357613:0.189804:0.357613:0.189804:0.342673:0.096840:0.342673:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 decrecimiento: si '( )es :@0.096840:0.372742:0.250875:0.372742:0.250875:0.357802:0.096840:0.357802:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 V t:@0.209258:0.372742:0.229121:0.372742:0.229121:0.357827:0.209258:0.357827:0.000000:0.000000:0.000000 positiva, las ventas están :@0.096823:0.387871:0.257261:0.387871:0.257261:0.372931:0.096823:0.372931:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 creciendo. si es negativa, :@0.096823:0.403000:0.259232:0.403000:0.259232:0.388060:0.096823:0.388060:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 las ventas están :@0.096823:0.418129:0.201320:0.418129:0.201320:0.403189:0.096823:0.403189:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 bajando. Esto permite :@0.096823:0.433258:0.241515:0.433258:0.241515:0.418318:0.096823:0.418318:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tomar decisiones :@0.096823:0.448386:0.210992:0.448386:0.210992:0.433447:0.096823:0.433447:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 rápidas, como :@0.096823:0.463515:0.191246:0.463515:0.191246:0.448576:0.096823:0.448576:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 intensificar campañas :@0.096823:0.478644:0.240111:0.478644:0.240111:0.463705:0.096823:0.463705:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de :@0.096823:0.493773:0.117239:0.493773:0.117239:0.478833:0.096823:0.478833:0.000000:0.000000:0.000000 marketing:@0.116988:0.493773:0.180834:0.493773:0.180834:0.478859:0.116988:0.478859:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 .:@0.180660:0.493773:0.183572:0.493773:0.183572:0.478833:0.180660:0.478833:0.000000 • Optimizar recursos: :@0.077860:0.508902:0.224245:0.508902:0.224245:0.493962:0.077860:0.493962:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 saber en qué períodos :@0.096840:0.524031:0.245146:0.524031:0.245146:0.509091:0.096840:0.509091:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 las ventas crecen más :@0.096840:0.539160:0.240156:0.539160:0.240156:0.524220:0.096840:0.524220:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 rápido puede ayudar a :@0.096840:0.554289:0.246518:0.554289:0.246518:0.539349:0.096840:0.539349:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 planificar mejor la :@0.096840:0.569418:0.214730:0.569418:0.214730:0.554478:0.096840:0.554478:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 producción, el :@0.096840:0.584547:0.192871:0.584547:0.192871:0.569607:0.096840:0.569607:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 inventario y la inversión :@0.096840:0.599676:0.251814:0.599676:0.251814:0.584736:0.096840:0.584736:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 en publicidad.:@0.096840:0.614805:0.188436:0.614805:0.188436:0.599865:0.096840:0.599865:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Cátedra de :@0.078581:0.155716:0.167902:0.155716:0.167902:0.138769:0.078581:0.138769:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 emprendimiento:@0.078581:0.172358:0.211098:0.172358:0.211098:0.155411:0.078581:0.155411:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 MUESTRA EDITORIAL:@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