121:@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
1.3 Reglas básicas de derivación de funciones algebraicas:@0.073089:0.564795:0.522734:0.564795:0.522734:0.547848:0.073089:0.547848:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La derivada de una función se puede obtener directamente al utilizar ciertas reglas básicas de derivación. :@0.073089:0.592157:0.831963:0.592157:0.831963:0.575723:0.073089:0.575723:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Estas nos ayudan a simplificar el proceso de derivación, ahorrar tiempo al derivar y disminuir el riesgo de :@0.073089:0.608799:0.831830:0.608799:0.831830:0.592365:0.073089:0.592365:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
equivocarnos cuando se trata de funciones largas.:@0.073089:0.625440:0.434874:0.625440:0.434874:0.609007:0.073089:0.609007:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para valores de | | no nulos y cada vez más próximos a 0, el cociente incremental se :@0.073089:0.136836:0.710547:0.136836:0.710547:0.120402:0.073089:0.120402:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.194834:0.136836:0.204333:0.136836:0.204333:0.120430:0.194834:0.120430:0.000000
aproxima cada vez a 10. Calculemos la distancia de 10 a  ( ), esto es,  (10,  ( )),   ≠ 0. Se :@0.073089:0.153478:0.710366:0.153478:0.710366:0.137044:0.073089:0.137044:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Q h:@0.472158:0.153478:0.498223:0.153478:0.498223:0.137072:0.472158:0.137072:0.000000:0.000000:0.000000
d:@0.565722:0.153478:0.574981:0.153478:0.574981:0.137072:0.565722:0.137072:0.000000
Q h h:@0.604009:0.153478:0.655605:0.153478:0.655605:0.137072:0.604009:0.137072:0.000000:0.000000:0.000000:0.000000:0.000000
tiene: :@0.073089:0.170120:0.117209:0.170120:0.117209:0.153686:0.073089:0.153686:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.168880:0.202377:0.178139:0.202377:0.178139:0.185971:0.168880:0.185971:0.000000
(10,  ( )) = | ( ) – 10| =     (32 + 24  + 8  +  ) + 2 – 10  = :@0.178065:0.202377:0.614587:0.202379:0.614587:0.185945:0.178065:0.185943:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Q h:@0.207738:0.202377:0.233839:0.202377:0.233839:0.185971:0.207738:0.185971:0.000000:0.000000:0.000000
Q h:@0.265978:0.202377:0.292080:0.202377:0.292080:0.185971:0.265978:0.185971:0.000000:0.000000:0.000000
|:@0.354262:0.207674:0.358164:0.207674:0.358164:0.178093:0.354262:0.178093:0.000000
1:@0.364657:0.194016:0.373640:0.194016:0.373640:0.177582:0.364657:0.177582:0.000000
4:@0.364657:0.210408:0.373640:0.210408:0.373640:0.193974:0.364657:0.193974:0.000000
h:@0.439335:0.202379:0.448833:0.202379:0.448833:0.185972:0.439335:0.185972:0.000000
h:@0.476444:0.202379:0.485942:0.202379:0.485942:0.185972:0.476444:0.185972:0.000000
2:@0.485885:0.196315:0.491122:0.196315:0.491122:0.186734:0.485885:0.186734:0.000000
h:@0.509870:0.202379:0.519368:0.202379:0.519368:0.185972:0.509870:0.185972:0.000000
3:@0.519298:0.196315:0.524535:0.196315:0.524535:0.186734:0.519298:0.186734:0.000000
|:@0.591806:0.207674:0.595708:0.207674:0.595708:0.178093:0.591806:0.178093:0.000000
|:@0.305288:0.239934:0.309191:0.239934:0.309191:0.210353:0.305288:0.210353:0.000000
6  + 2  +     ,   ≠ 0.:@0.309109:0.234639:0.474165:0.234639:0.474165:0.218205:0.309109:0.218205:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.318018:0.234639:0.327516:0.234639:0.327516:0.218232:0.318018:0.218232:0.000000
h:@0.355127:0.234639:0.364625:0.234639:0.364625:0.218232:0.355127:0.218232:0.000000
2:@0.364568:0.228575:0.369805:0.228575:0.369805:0.218994:0.364568:0.218994:0.000000
1:@0.391172:0.226275:0.400154:0.226275:0.400154:0.209841:0.391172:0.209841:0.000000
4:@0.391172:0.242667:0.400154:0.242667:0.400154:0.226233:0.391172:0.226233:0.000000
h h:@0.406652:0.234637:0.443314:0.234639:0.443314:0.218232:0.406652:0.218231:0.000000:0.000000:0.000000
3:@0.416080:0.228575:0.421317:0.228575:0.421317:0.218994:0.416080:0.218994:0.000000
|:@0.421271:0.239934:0.425173:0.239934:0.425173:0.210353:0.421271:0.210353:0.000000
Observamos que para | | no nulo y suficientemente pequeño,:@0.073089:0.265578:0.522381:0.265578:0.522381:0.249145:0.073089:0.249145:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.241074:0.265578:0.250572:0.265578:0.250572:0.249172:0.241074:0.249172:0.000000
| | < 1,  (10,  ( )) =  6  + 2  +   :@0.073089:0.297947:0.325290:0.297943:0.325290:0.281509:0.073089:0.281513:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.076955:0.297947:0.086453:0.297947:0.086453:0.281541:0.076955:0.281541:0.000000
d:@0.126526:0.297947:0.135784:0.297947:0.135784:0.281541:0.126526:0.281541:0.000000
Q h:@0.166083:0.297947:0.192258:0.297947:0.192258:0.281541:0.166083:0.281541:0.000000:0.000000:0.000000
|:@0.221664:0.303233:0.225567:0.303233:0.225567:0.273652:0.221664:0.273652:0.000000
h:@0.234477:0.297938:0.243976:0.297938:0.243976:0.281532:0.234477:0.281532:0.000000
h:@0.272617:0.297938:0.282115:0.297938:0.282115:0.281532:0.272617:0.281532:0.000000
2:@0.282104:0.291874:0.287341:0.291874:0.287341:0.282293:0.282104:0.282293:0.000000
1:@0.309681:0.290468:0.318664:0.290468:0.318664:0.274034:0.309681:0.274034:0.000000
4:@0.309681:0.306860:0.318664:0.306860:0.318664:0.290426:0.309681:0.290426:0.000000
h:@0.325659:0.297943:0.335157:0.297943:0.335157:0.281537:0.325659:0.281537:0.000000
3 :@0.335122:0.291874:0.342687:0.291874:0.342687:0.282293:0.335122:0.282293:0.000000:0.000000
| :@0.342903:0.303233:0.350800:0.303233:0.350800:0.273652:0.342903:0.273652:0.000000:0.000000
es también suficientemente pequeño. En efecto, :@0.351171:0.297938:0.710297:0.297938:0.710297:0.281504:0.351171:0.281504:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sea   > 0. Entonces, como 0 < | | <   ≤ | |, y por la desigualdad triangular, se tiene: :@0.073093:0.323150:0.680861:0.323153:0.680861:0.306719:0.073093:0.306717:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ε:@0.100943:0.322734:0.109024:0.322734:0.109024:0.305746:0.100943:0.305746:0.000000
h:@0.295618:0.323150:0.305116:0.323150:0.305116:0.306744:0.295618:0.306744:0.000000
3:@0.305056:0.317089:0.310293:0.317089:0.310293:0.307508:0.305056:0.307508:0.000000
h:@0.332851:0.323153:0.342349:0.323153:0.342349:0.306747:0.332851:0.306747:0.000000
2:@0.342290:0.317089:0.347527:0.317089:0.347527:0.307508:0.342290:0.307508:0.000000
h:@0.370085:0.323153:0.379584:0.323153:0.379584:0.306747:0.370085:0.306747:0.000000
d:@0.165838:0.375062:0.175097:0.375062:0.175097:0.358655:0.165838:0.358655:0.000000
(10,  ( )) =  6  + 2  +     ≤ 6| | + 2  +  4  | |  < :@0.175024:0.375062:0.544069:0.375067:0.544069:0.358633:0.175024:0.358628:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Q h:@0.204696:0.375062:0.230798:0.375062:0.230798:0.358655:0.204696:0.358655:0.000000:0.000000:0.000000
|:@0.259142:0.380362:0.263044:0.380362:0.263044:0.350781:0.259142:0.350781:0.000000
h:@0.271873:0.375067:0.281371:0.375067:0.281371:0.358661:0.271873:0.358661:0.000000
h:@0.308982:0.375067:0.318480:0.375067:0.318480:0.358661:0.308982:0.358661:0.000000
2:@0.318421:0.369003:0.323658:0.369003:0.323658:0.359422:0.318421:0.359422:0.000000
1:@0.345026:0.366704:0.354009:0.366704:0.354009:0.350270:0.345026:0.350270:0.000000
4:@0.345026:0.383096:0.354009:0.383096:0.354009:0.366662:0.345026:0.366662:0.000000
h:@0.360507:0.375067:0.370005:0.375067:0.370005:0.358661:0.360507:0.358661:0.000000
3:@0.369935:0.369003:0.375172:0.369003:0.375172:0.359422:0.369935:0.359422:0.000000
|:@0.375124:0.380362:0.379026:0.380362:0.379026:0.350781:0.375124:0.350781:0.000000
h:@0.410459:0.375067:0.419957:0.375067:0.419957:0.358661:0.410459:0.358661:0.000000
h:@0.451397:0.375067:0.460895:0.375067:0.460895:0.358661:0.451397:0.358661:0.000000
2:@0.460838:0.369003:0.466075:0.369003:0.466075:0.359422:0.460838:0.359422:0.000000
1:@0.487443:0.357769:0.496426:0.357769:0.496426:0.341335:0.487443:0.341335:0.000000
h:@0.506734:0.375063:0.516232:0.375063:0.516232:0.358657:0.506734:0.358657:0.000000
3:@0.519994:0.369003:0.525231:0.369003:0.525231:0.359422:0.519994:0.359422:0.000000
33:@0.544519:0.367598:0.562411:0.367598:0.562411:0.351164:0.544519:0.351164:0.000000:0.000000
4:@0.548974:0.383990:0.557956:0.383990:0.557956:0.367556:0.548974:0.367556:0.000000
 | | < ε, :@0.562871:0.375073:0.617633:0.375073:0.617633:0.358639:0.562871:0.358639:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.570639:0.375073:0.580137:0.375073:0.580137:0.358667:0.570639:0.358667:0.000000
de donde 0 < | | < :@0.073073:0.406443:0.211624:0.406443:0.211624:0.390009:0.073073:0.390009:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.179485:0.406443:0.188983:0.406443:0.188983:0.390037:0.179485:0.390037:0.000000
4ε:@0.215064:0.398963:0.231741:0.398963:0.231741:0.382529:0.215064:0.382529:0.000000:0.000000
33:@0.214457:0.415355:0.232349:0.415355:0.232349:0.398921:0.214457:0.398921:0.000000:0.000000
 . Así, 0 < | | < :@0.235184:0.406438:0.338025:0.406438:0.338025:0.390004:0.235184:0.390004:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.305886:0.406438:0.315384:0.406438:0.315384:0.390032:0.305886:0.390032:0.000000
4ε:@0.341449:0.398963:0.358126:0.398963:0.358126:0.382529:0.341449:0.382529:0.000000:0.000000
33:@0.340841:0.415355:0.358733:0.415355:0.358733:0.398921:0.340841:0.398921:0.000000:0.000000
 :@0.361568:0.406438:0.365599:0.406438:0.365599:0.390004:0.361568:0.390004:0.000000
 :@0.381255:0.406017:0.385857:0.406017:0.385857:0.389028:0.381255:0.389028:0.000000
d:@0.385765:0.406433:0.395024:0.406433:0.395024:0.390027:0.385765:0.390027:0.000000
(10,  ( )) < ε, que significa que: :@0.394950:0.406433:0.624778:0.406433:0.624778:0.389999:0.394950:0.389999:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Q h:@0.424623:0.406433:0.450724:0.406433:0.450724:0.390027:0.424623:0.390027:0.000000:0.000000:0.000000
lím  :@0.161068:0.448523:0.189599:0.448523:0.189599:0.432117:0.161068:0.432117:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.189562:0.448523:0.193593:0.448523:0.193593:0.432089:0.189562:0.432089:0.000000
p  + h:@0.200797:0.441050:0.250552:0.441050:0.250552:0.424644:0.200797:0.424644:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(2:@0.209982:0.441050:0.223769:0.441050:0.223769:0.424616:0.209982:0.424616:0.000000:0.000000
) –  (2):@0.250515:0.441050:0.300104:0.441050:0.300104:0.424616:0.250515:0.424616:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.272328:0.441050:0.281587:0.441050:0.281587:0.424644:0.272328:0.424644:0.000000
h:@0.245692:0.457442:0.255191:0.457442:0.255191:0.441036:0.245692:0.441036:0.000000
 =   :@0.307283:0.448525:0.334084:0.448525:0.334084:0.432091:0.307283:0.432091:0.000000:0.000000:0.000000:0.000000:0.000000
lím        :@0.333974:0.448525:0.393866:0.448529:0.393866:0.432123:0.333974:0.432119:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.379011:0.443731:0.387994:0.443731:0.387994:0.427297:0.379011:0.427297:0.000000
4:@0.379011:0.460123:0.387994:0.460123:0.387994:0.443689:0.379011:0.443689:0.000000
(32 + 24  + 8  +  ) + 2   = 10.:@0.393792:0.448529:0.618428:0.448520:0.618428:0.432086:0.393792:0.432095:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.452990:0.448529:0.462488:0.448529:0.462488:0.432123:0.452990:0.432123:0.000000
h:@0.490099:0.448529:0.499597:0.448529:0.499597:0.432123:0.490099:0.432123:0.000000
2:@0.499550:0.442456:0.504787:0.442456:0.504787:0.432875:0.499550:0.432875:0.000000
h:@0.523535:0.448520:0.533033:0.448520:0.533033:0.432114:0.523535:0.432114:0.000000
3:@0.532963:0.442456:0.538200:0.442456:0.538200:0.432875:0.532963:0.432875:0.000000
A este número real se le llama :@0.073094:0.483024:0.293446:0.483024:0.293446:0.466590:0.073094:0.466590:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
derivada:@0.293171:0.483024:0.359557:0.483024:0.359557:0.466355:0.293171:0.466355:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 de la función   en el punto:@0.359456:0.483024:0.559002:0.483024:0.559002:0.466590:0.359456:0.466590:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.461745:0.483024:0.471004:0.483024:0.471004:0.466618:0.461745:0.466618:0.000000
x:@0.073076:0.509027:0.080531:0.509027:0.080531:0.492621:0.073076:0.492621:0.000000
 = 2. Se escribe :@0.080457:0.509027:0.192635:0.509027:0.192635:0.492593:0.080457:0.492593:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dp:@0.195108:0.503352:0.213552:0.503352:0.213552:0.486946:0.195108:0.486946:0.000000:0.000000
dx:@0.196010:0.519745:0.212650:0.519745:0.212650:0.503339:0.196010:0.503339:0.000000:0.000000
 (2) = 10.:@0.216110:0.509038:0.278419:0.509038:0.278419:0.492605:0.216110:0.492605:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.158471:0.458529:0.164947:0.458529:0.164947:0.447343:0.158471:0.447343:0.000000
→:@0.164901:0.457968:0.175637:0.457968:0.175637:0.447929:0.164901:0.447929:0.000000
0:@0.175581:0.458529:0.181706:0.458529:0.181706:0.447324:0.175581:0.447324:0.000000
h:@0.330566:0.458302:0.337042:0.458302:0.337042:0.447116:0.330566:0.447116:0.000000
→:@0.336991:0.457741:0.347726:0.457741:0.347726:0.447703:0.336991:0.447703:0.000000
0:@0.347670:0.458302:0.353795:0.458302:0.353795:0.447097:0.347670:0.447097:0.000000
Nombre:@0.148251:0.653930:0.205615:0.653930:0.205615:0.638775:0.148251:0.638775:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Regla:@0.426435:0.653930:0.465258:0.653930:0.465258:0.638775:0.426435:0.638775:0.000000:0.000000:0.000000:0.000000:0.000000
Ejemplos:@0.737367:0.653930:0.801290:0.653930:0.801290:0.638775:0.737367:0.638775:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Derivada de una constante:@0.081410:0.681295:0.237647:0.681295:0.237647:0.667849:0.081410:0.667849:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sea   una constante,  ( )= ;   '( )=0:@0.287015:0.681295:0.492213:0.681295:0.492213:0.667849:0.287015:0.667849:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c:@0.311519:0.681295:0.317784:0.681295:0.317784:0.667872:0.311519:0.667872:0.000000
f x c f x:@0.412904:0.681295:0.471896:0.681295:0.471896:0.667872:0.412904:0.667872:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.619220:0.681295:0.633150:0.681295:0.633150:0.667872:0.619220:0.667872:0.000000:0.000000:0.000000
( )= 9;   ( )=0:@0.623060:0.681295:0.700230:0.681295:0.700230:0.667849:0.623060:0.667849:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.665982:0.681295:0.679913:0.681295:0.679913:0.667872:0.665982:0.667872:0.000000:0.000000:0.000000
Derivada de una potencia:@0.081395:0.715801:0.232704:0.715801:0.232704:0.702355:0.081395:0.702355:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sea     :@0.287000:0.717117:0.338417:0.717117:0.338417:0.703671:0.287000:0.703671:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.311504:0.717117:0.319275:0.717117:0.319275:0.703694:0.311504:0.703694:0.000000
∈ ℤ:@0.322573:0.717593:0.348462:0.717593:0.348462:0.703149:0.322573:0.703149:0.000000:0.000000:0.000000
+:@0.348479:0.712427:0.355793:0.712427:0.355793:0.704006:0.348479:0.704006:0.000000
 y  ( )=:@0.355793:0.717111:0.395914:0.717111:0.395914:0.703665:0.355793:0.703665:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x x , f'  x nx  :@0.369016:0.717111:0.474819:0.717111:0.474819:0.703687:0.369016:0.703687:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.402014:0.712149:0.406544:0.712149:0.406544:0.704323:0.402014:0.704323:0.000000
( )=:@0.421800:0.717111:0.444857:0.717111:0.444857:0.703665:0.421800:0.703665:0.000000:0.000000:0.000000:0.000000
n 1:@0.458726:0.712149:0.472107:0.712149:0.472107:0.704310:0.458726:0.704310:0.000000:0.000000:0.000000
–:@0.463433:0.712427:0.467823:0.712427:0.467823:0.704006:0.463433:0.704006:0.000000
f x:@0.619234:0.715794:0.633165:0.715794:0.633165:0.702371:0.619234:0.702371:0.000000:0.000000:0.000000
( )= x ;   ( )=5x:@0.623075:0.715794:0.713362:0.715799:0.713362:0.702353:0.623075:0.702348:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.655885:0.710838:0.660169:0.710838:0.660169:0.702999:0.655885:0.702999:0.000000
f' x:@0.669386:0.715799:0.686585:0.715799:0.686585:0.702376:0.669386:0.702376:0.000000:0.000000:0.000000:0.000000
4:@0.713361:0.710838:0.717645:0.710838:0.717645:0.702999:0.713361:0.702999:0.000000
Derivada del producto de una :@0.081410:0.747735:0.258655:0.747735:0.258655:0.734289:0.081410:0.734289:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
constante por una función:@0.081410:0.760341:0.235372:0.760341:0.235372:0.746896:0.081410:0.746896:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sea   una constante:  ( )= ( ):@0.287015:0.740428:0.468012:0.740428:0.468012:0.726982:0.287015:0.726982:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c:@0.311519:0.740428:0.317784:0.740428:0.317784:0.727005:0.311519:0.727005:0.000000
g x cf x:@0.413055:0.740428:0.464021:0.740428:0.464021:0.727005:0.413055:0.727005:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g' x cf' x:@0.287015:0.753034:0.343462:0.753034:0.343462:0.739611:0.287015:0.739611:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( )= ( ):@0.296805:0.753034:0.347453:0.753034:0.347453:0.739588:0.296805:0.739588:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.619220:0.745954:0.633150:0.745954:0.633150:0.732531:0.619220:0.732531:0.000000:0.000000:0.000000
( )= 2:@0.623060:0.745954:0.656765:0.745954:0.656765:0.732508:0.623060:0.732508:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.656765:0.745954:0.662865:0.745954:0.662865:0.732531:0.656765:0.732531:0.000000
5:@0.662873:0.740987:0.667158:0.740987:0.667158:0.733149:0.662873:0.733149:0.000000
f' x:@0.619228:0.762129:0.636427:0.762129:0.636427:0.748706:0.619228:0.748706:0.000000:0.000000:0.000000:0.000000
( )= 2.5x ;  ( ) = 10:@0.626336:0.762129:0.740516:0.762129:0.740516:0.748683:0.626336:0.748683:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4:@0.676471:0.757168:0.680755:0.757168:0.680755:0.749329:0.676471:0.749329:0.000000
f´ x:@0.686675:0.762129:0.706254:0.762129:0.706254:0.748706:0.686675:0.748706:0.000000:0.000000:0.000000:0.000000
x:@0.740516:0.762129:0.746616:0.762129:0.746616:0.748706:0.740516:0.748706:0.000000
4:@0.746614:0.757168:0.750899:0.757168:0.750899:0.749329:0.746614:0.749329:0.000000
Derivada de la suma o  :@0.081410:0.790263:0.216066:0.790263:0.216066:0.776817:0.081410:0.776817:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
diferencia de funciones:@0.081410:0.802869:0.216141:0.802869:0.216141:0.789423:0.081410:0.789423:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean  ,   dos funciones y   definida por::@0.287018:0.784026:0.524325:0.784026:0.524325:0.770580:0.287018:0.770580:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f g:@0.319594:0.784026:0.336929:0.784026:0.336929:0.770603:0.319594:0.770603:0.000000:0.000000:0.000000
h:@0.437458:0.784026:0.445229:0.784026:0.445229:0.770603:0.437458:0.770603:0.000000
h x f x:@0.287018:0.800206:0.331778:0.800206:0.331778:0.786783:0.287018:0.786783:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( )= ( ) +  ( ),  ( )= ( ) +  ( ):@0.294790:0.800206:0.472006:0.800206:0.472006:0.786760:0.294790:0.786760:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g x h' x f' x:@0.351342:0.800206:0.428572:0.800206:0.428572:0.786783:0.351342:0.786783:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g' x:@0.448135:0.800206:0.468015:0.800206:0.468015:0.786783:0.448135:0.786783:0.000000:0.000000:0.000000:0.000000
h x:@0.619223:0.789790:0.637084:0.789790:0.637084:0.776367:0.619223:0.776367:0.000000:0.000000:0.000000
( )= x    2  + 3:@0.626994:0.789790:0.718881:0.789787:0.718881:0.776342:0.626994:0.776344:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.659816:0.784826:0.664100:0.784826:0.664100:0.776987:0.659816:0.776987:0.000000
–:@0.667398:0.790264:0.674928:0.790264:0.674928:0.775820:0.667398:0.775820:0.000000
x:@0.685576:0.789787:0.691675:0.789787:0.691675:0.776364:0.685576:0.776364:0.000000
2:@0.691675:0.784826:0.695960:0.784826:0.695960:0.776987:0.691675:0.776987:0.000000
h' x:@0.619226:0.805968:0.638714:0.805968:0.638714:0.792545:0.619226:0.792545:0.000000:0.000000:0.000000:0.000000
( )= 3    4:@0.628624:0.805968:0.694190:0.805968:0.694190:0.792522:0.628624:0.792522:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.662329:0.805968:0.668428:0.805968:0.668428:0.792545:0.662329:0.792545:0.000000
2:@0.668430:0.801006:0.672715:0.801006:0.672715:0.793168:0.668430:0.793168:0.000000
–:@0.676012:0.806444:0.683542:0.806444:0.683542:0.792000:0.676012:0.792000:0.000000
x:@0.694190:0.805968:0.700290:0.805968:0.700290:0.792545:0.694190:0.792545:0.000000
Derivada del producto de dos :@0.081409:0.835469:0.257570:0.835469:0.257570:0.822023:0.081409:0.822023:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
funciones:@0.081409:0.848075:0.138489:0.848075:0.138489:0.834630:0.081409:0.834630:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean  ,   dos funciones y   definida por::@0.287015:0.825473:0.524322:0.825473:0.524322:0.812027:0.287015:0.812027:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f g:@0.319591:0.825473:0.336926:0.825473:0.336926:0.812050:0.319591:0.812050:0.000000:0.000000:0.000000
h:@0.437454:0.825473:0.445225:0.825473:0.445225:0.812050:0.437454:0.812050:0.000000
h x f x g x h´ x f x g´ x:@0.287015:0.845227:0.461687:0.845227:0.461687:0.831804:0.287015:0.831804:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( )= ( ) •  ( );  ( )= ( ) •  ( ) +  ( ) •  ( ):@0.294786:0.845227:0.534414:0.845227:0.534414:0.831782:0.294786:0.831782:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g x f' x:@0.481250:0.845227:0.530423:0.845227:0.530423:0.831804:0.481250:0.831804:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h x:@0.619234:0.828684:0.637096:0.828684:0.637096:0.815261:0.619234:0.815261:0.000000:0.000000:0.000000
( )=   (:@0.627005:0.828684:0.671027:0.828691:0.671027:0.815246:0.627005:0.815238:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x x:@0.653361:0.828684:0.677127:0.828691:0.677127:0.815268:0.653361:0.815261:0.000000:0.000000:0.000000
5:@0.659454:0.823730:0.663739:0.823730:0.663739:0.815891:0.659454:0.815891:0.000000
2 :@0.677127:0.823730:0.683334:0.823730:0.683334:0.815891:0.677127:0.815891:0.000000:0.000000
–:@0.683335:0.829168:0.690865:0.829168:0.690865:0.814724:0.683335:0.814724:0.000000
 2):@0.690865:0.828691:0.705504:0.828691:0.705504:0.815246:0.690865:0.815246:0.000000:0.000000:0.000000
h' x:@0.619223:0.843090:0.638711:0.843090:0.638711:0.829667:0.619223:0.829667:0.000000:0.000000:0.000000:0.000000
( )=   (2 ) + (:@0.628620:0.843090:0.709657:0.843085:0.709657:0.829640:0.628620:0.829645:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.654976:0.843090:0.661076:0.843090:0.661076:0.829667:0.654976:0.829667:0.000000
5:@0.661081:0.838124:0.665365:0.838124:0.665365:0.830285:0.661081:0.830285:0.000000
x:@0.680003:0.843085:0.686103:0.843085:0.686103:0.829662:0.680003:0.829662:0.000000
x:@0.709657:0.843085:0.715757:0.843085:0.715757:0.829662:0.709657:0.829662:0.000000
2 :@0.715757:0.838124:0.721964:0.838124:0.721964:0.830285:0.715757:0.830285:0.000000:0.000000
–:@0.721963:0.843562:0.729494:0.843562:0.729494:0.829118:0.721963:0.829118:0.000000
 2) 5:@0.729494:0.843085:0.754780:0.843085:0.754780:0.829640:0.729494:0.829640:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.754780:0.843085:0.760880:0.843085:0.760880:0.829662:0.754780:0.829662:0.000000
4:@0.760880:0.838124:0.765164:0.838124:0.765164:0.830285:0.760880:0.830285:0.000000
h' x:@0.619228:0.857479:0.638716:0.857479:0.638716:0.844056:0.619228:0.844056:0.000000:0.000000:0.000000:0.000000
( )= 7:@0.628625:0.857479:0.662331:0.857479:0.662331:0.844033:0.628625:0.844033:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.662331:0.857479:0.668430:0.857479:0.668430:0.844056:0.662331:0.844056:0.000000
6 :@0.668430:0.852518:0.674638:0.852518:0.674638:0.844679:0.668430:0.844679:0.000000:0.000000
–:@0.674637:0.857956:0.682167:0.857956:0.682167:0.843512:0.674637:0.843512:0.000000
 10:@0.682167:0.857479:0.700164:0.857479:0.700164:0.844033:0.682167:0.844033:0.000000:0.000000:0.000000
x:@0.700164:0.857479:0.706264:0.857479:0.706264:0.844056:0.700164:0.844056:0.000000
4:@0.706264:0.852518:0.710548:0.852518:0.710548:0.844679:0.706264:0.844679:0.000000
Derivada del cociente de dos :@0.081410:0.896325:0.253158:0.896325:0.253158:0.882880:0.081410:0.882880:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
funciones:@0.081410:0.908932:0.138489:0.908932:0.138489:0.895486:0.081410:0.895486:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean  ,   dos funciones y   definida por::@0.287016:0.874438:0.524322:0.874438:0.524322:0.860992:0.287016:0.860992:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f g:@0.319591:0.874438:0.336926:0.874438:0.336926:0.861014:0.319591:0.861014:0.000000:0.000000:0.000000
h:@0.437455:0.874438:0.445226:0.874438:0.445226:0.861014:0.437455:0.861014:0.000000
h x:@0.287016:0.901341:0.304877:0.901341:0.304877:0.887917:0.287016:0.887917:0.000000:0.000000:0.000000
( )= :@0.294787:0.901341:0.321143:0.901341:0.321143:0.887895:0.294787:0.887895:0.000000:0.000000:0.000000:0.000000:0.000000
f(x):@0.323483:0.892164:0.341224:0.892164:0.341224:0.878741:0.323483:0.878741:0.000000:0.000000:0.000000:0.000000
g(x):@0.321616:0.908548:0.343092:0.908548:0.343092:0.895125:0.321616:0.895125:0.000000:0.000000:0.000000:0.000000
;  ( )≠0;  ( )= :@0.343574:0.901343:0.427521:0.901343:0.427521:0.887897:0.343574:0.887897:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g x:@0.349493:0.901343:0.367159:0.901343:0.367159:0.887920:0.349493:0.887920:0.000000:0.000000:0.000000
h x:@0.393394:0.901343:0.411256:0.901343:0.411256:0.887920:0.393394:0.887920:0.000000:0.000000:0.000000
g(x)   f'(x)   f(x)   g'(x):@0.434395:0.892645:0.548795:0.892645:0.548795:0.879222:0.434395:0.879222:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
•:@0.458492:0.892645:0.462212:0.892645:0.462212:0.879199:0.458492:0.879199:0.000000
–:@0.488387:0.893122:0.495917:0.893122:0.495917:0.878677:0.488387:0.878677:0.000000
•:@0.518854:0.892645:0.522574:0.892645:0.522574:0.879199:0.518854:0.879199:0.000000
[:@0.474833:0.909030:0.478824:0.909030:0.478824:0.895584:0.474833:0.895584:0.000000
g(x):@0.478763:0.909030:0.500240:0.909030:0.500240:0.895607:0.478763:0.895607:0.000000:0.000000:0.000000:0.000000
]:@0.500210:0.909030:0.504201:0.909030:0.504201:0.895584:0.500210:0.895584:0.000000
2:@0.504107:0.904074:0.508392:0.904074:0.508392:0.896235:0.504107:0.896235:0.000000
h x:@0.619228:0.890105:0.637089:0.890105:0.637089:0.876682:0.619228:0.876682:0.000000:0.000000:0.000000
( )= :@0.626999:0.890105:0.653355:0.890105:0.653355:0.876659:0.626999:0.876659:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.655356:0.883724:0.661455:0.883724:0.661455:0.870301:0.655356:0.870301:0.000000
2 :@0.661400:0.878763:0.667573:0.878763:0.667573:0.870924:0.661400:0.870924:0.000000:0.000000
+:@0.667532:0.884201:0.680077:0.884201:0.680077:0.869756:0.667532:0.869756:0.000000
 2:@0.680002:0.883724:0.690589:0.883724:0.690589:0.870278:0.680002:0.870278:0.000000:0.000000
x:@0.659037:0.896330:0.665137:0.896330:0.665137:0.882907:0.659037:0.882907:0.000000
  :@0.665090:0.891370:0.668901:0.891370:0.668901:0.883531:0.665090:0.883531:0.000000:0.000000
–:@0.668859:0.896808:0.676389:0.896808:0.676389:0.882364:0.668859:0.882364:0.000000
 1:@0.676313:0.896332:0.686901:0.896332:0.686901:0.882886:0.676313:0.882886:0.000000:0.000000
,  ( )= :@0.692579:0.890102:0.734251:0.890102:0.734251:0.876657:0.692579:0.876657:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h' x:@0.698498:0.890102:0.717986:0.890102:0.717986:0.876679:0.698498:0.876679:0.000000:0.000000:0.000000:0.000000
(:@0.748088:0.883724:0.752079:0.883724:0.752079:0.870278:0.748088:0.870278:0.000000
x :@0.752019:0.883724:0.760769:0.883724:0.760769:0.870301:0.752019:0.870301:0.000000:0.000000
 :@0.760716:0.878763:0.762639:0.878763:0.762639:0.870924:0.760716:0.870924:0.000000
–:@0.762600:0.884201:0.770130:0.884201:0.770130:0.869756:0.762600:0.869756:0.000000
 1) (2x)   (:@0.770055:0.883724:0.827179:0.883724:0.827179:0.870278:0.770055:0.870278:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.812495:0.884201:0.820026:0.884201:0.820026:0.869756:0.812495:0.869756:0.000000
x:@0.827104:0.883724:0.833204:0.883724:0.833204:0.870301:0.827104:0.870301:0.000000
2 :@0.833145:0.878763:0.839317:0.878763:0.839317:0.870924:0.833145:0.870924:0.000000:0.000000
+:@0.839276:0.884201:0.851822:0.884201:0.851822:0.869756:0.839276:0.869756:0.000000
 2) (1) :@0.851746:0.883724:0.887952:0.883724:0.887952:0.870278:0.851746:0.870278:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.796007:0.896330:0.799998:0.896330:0.799998:0.882885:0.796007:0.882885:0.000000
x :@0.799938:0.896330:0.808688:0.896330:0.808688:0.882907:0.799938:0.882907:0.000000:0.000000
 :@0.808635:0.891370:0.810558:0.891370:0.810558:0.883531:0.808635:0.883531:0.000000
–:@0.810519:0.896808:0.818049:0.896808:0.818049:0.882364:0.810519:0.882364:0.000000
 1):@0.817974:0.896332:0.832492:0.896332:0.832492:0.882886:0.817974:0.882886:0.000000:0.000000:0.000000
2:@0.832415:0.891370:0.836700:0.891370:0.836700:0.883531:0.832415:0.883531:0.000000
, :@0.898451:0.890105:0.904369:0.890105:0.904369:0.876659:0.898451:0.876659:0.000000:0.000000
h' x:@0.619229:0.924156:0.638717:0.924156:0.638717:0.910733:0.619229:0.910733:0.000000:0.000000:0.000000:0.000000
( )= :@0.628627:0.924156:0.654983:0.924156:0.654983:0.910711:0.628627:0.910711:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.658405:0.915729:0.664504:0.915729:0.664504:0.902306:0.658405:0.902306:0.000000
2 :@0.664451:0.910768:0.670623:0.910768:0.670623:0.902929:0.664451:0.902929:0.000000:0.000000
–:@0.670580:0.916206:0.678111:0.916206:0.678111:0.901762:0.670580:0.901762:0.000000
 2x  2:@0.678035:0.915729:0.716741:0.915729:0.716741:0.902284:0.678035:0.902284:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
– :@0.698171:0.916206:0.709391:0.916206:0.709391:0.901762:0.698171:0.901762:0.000000:0.000000
(:@0.667192:0.928336:0.671183:0.928336:0.671183:0.914890:0.667192:0.914890:0.000000
x :@0.671123:0.928336:0.679873:0.928336:0.679873:0.914912:0.671123:0.914912:0.000000:0.000000
 :@0.679819:0.923375:0.681742:0.923375:0.681742:0.915537:0.679819:0.915537:0.000000
–:@0.681703:0.928813:0.689234:0.928813:0.689234:0.914369:0.681703:0.914369:0.000000
 1):@0.689158:0.928337:0.703677:0.928337:0.703677:0.914891:0.689158:0.914891:0.000000:0.000000:0.000000
2:@0.703600:0.923375:0.707884:0.923375:0.707884:0.915537:0.703600:0.915537:0.000000
El concepto de derivada de :@0.741105:0.199684:0.924395:0.199684:0.924395:0.184745:0.741105:0.184745:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
una función real contiene :@0.741105:0.214813:0.913894:0.214813:0.913894:0.199873:0.741105:0.199873:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la existencia del límite :@0.741105:0.229942:0.889304:0.229942:0.889304:0.215002:0.741105:0.215002:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
del cociente incremental :@0.741105:0.245071:0.908814:0.245071:0.908814:0.230131:0.741105:0.230131:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y sus aplicaciones. Una :@0.741105:0.260200:0.894915:0.260200:0.894915:0.245260:0.741105:0.245260:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de las primeras fue hallar :@0.741105:0.275329:0.908320:0.275329:0.908320:0.260389:0.741105:0.260389:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la ecuación de la recta :@0.741105:0.290458:0.891628:0.290458:0.891628:0.275518:0.741105:0.275518:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tangente a la gráfica de :@0.741105:0.305587:0.899396:0.305587:0.899396:0.290647:0.741105:0.290647:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
una curva en un punto :@0.741105:0.320716:0.896483:0.320716:0.896483:0.305776:0.741105:0.305776:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
asignado.:@0.741105:0.335845:0.804045:0.335845:0.804045:0.320905:0.741105:0.320905:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Los primeros trabajos :@0.741105:0.356332:0.885860:0.356332:0.885860:0.341392:0.741105:0.341392:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en esta dirección fueron :@0.741105:0.371461:0.904199:0.371461:0.904199:0.356521:0.741105:0.356521:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
realizados por Fermat, :@0.741105:0.386590:0.889565:0.386590:0.889565:0.371650:0.741105:0.371650:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Newton, Leibniz, entre :@0.741105:0.401719:0.892771:0.401719:0.892771:0.386779:0.741105:0.386779:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
otros, pero fue Fermat :@0.741105:0.416848:0.890222:0.416848:0.890222:0.401908:0.741105:0.401908:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
quien obtuvo un método :@0.741105:0.431977:0.913083:0.431977:0.913083:0.417037:0.741105:0.417037:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
para hallar la ecuación :@0.741105:0.447106:0.891894:0.447106:0.891894:0.432166:0.741105:0.432166:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de la recta tangente a :@0.741105:0.462235:0.888360:0.462235:0.888360:0.447295:0.741105:0.447295:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
una curva definida por :@0.741105:0.477363:0.894095:0.477363:0.894095:0.462424:0.741105:0.462424:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
una función polinomial :@0.741105:0.492492:0.898620:0.492492:0.898620:0.477553:0.741105:0.477553:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mediante el análisis del :@0.741105:0.507621:0.898012:0.507621:0.898012:0.492682:0.741105:0.492682:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cociente incremental.:@0.741105:0.522750:0.883643:0.522750:0.883643:0.507810:0.741105:0.507810:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Interdisciplinaria :@0.740285:0.141148:0.863694:0.141148:0.863694:0.125742:0.740285:0.125742:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Matemática e :@0.740285:0.156277:0.833948:0.156277:0.833948:0.141337:0.740285:0.141337:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
historia:@0.740285:0.171406:0.788633:0.171406:0.788633:0.156466:0.740285:0.156466:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
DBA 3 (Ev. 2) Utiliza e interpreta la derivada para resolver problemas relacionados con la variación y la razón de cambio de :@0.086015:0.965315:0.727410:0.965315:0.727410:0.953363:0.086015:0.953363:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
funciones que involucran magnitudes como velocidad, aceleración, longitud, tiempo.:@0.086015:0.977418:0.535814:0.977418:0.535814:0.965466:0.086015:0.965466:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
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