130:@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 La derivada de las funciones trigonométricas tiene diversas aplicaciones en diferentes :@0.293660:0.251197:0.931356:0.251197:0.931356:0.234763:0.293660:0.234763:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 campos de la física, la ingeniería, el cálculo integral, así como en las ecuaciones :@0.293660:0.267839:0.930748:0.267839:0.930748:0.251405:0.293660:0.251405:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 diferenciales y en la economía.:@0.293660:0.284481:0.515243:0.284481:0.515243:0.268047:0.293660:0.268047:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3.1 Derivada de la función seno :@0.293660:0.311843:0.543482:0.311843:0.543482:0.294896:0.293660:0.294896:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Sea ( ) = :@0.293660:0.339205:0.363773:0.339205:0.363773:0.322771:0.293660:0.322771:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x:@0.323277:0.339205:0.340157:0.339205:0.340157:0.322799:0.323277:0.322799:0.000000:0.000000:0.000000 sen x:@0.363663:0.339205:0.398526:0.339205:0.398526:0.322799:0.363663:0.322799:0.000000:0.000000:0.000000:0.000000:0.000000 , por :@0.387114:0.339205:0.434733:0.339205:0.434733:0.322771:0.387114:0.322771:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tan:@0.434623:0.339205:0.458608:0.339205:0.458608:0.322799:0.434623:0.322799:0.000000:0.000000:0.000000 to ( + ) = :@0.458552:0.339205:0.545729:0.339205:0.545729:0.322771:0.458552:0.322771:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x h:@0.477714:0.339205:0.522113:0.339205:0.522113:0.322799:0.477714:0.322799:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 sen x h:@0.545619:0.339205:0.612787:0.339205:0.612787:0.322799:0.545619:0.322799:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( + ).:@0.569069:0.339205:0.620720:0.339205:0.620720:0.322771:0.569069:0.322771:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Si aplicamos la definición de derivada de una función ´( ) = :@0.293605:0.371421:0.740239:0.371421:0.740239:0.354987:0.293605:0.354987:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x:@0.693153:0.371421:0.715757:0.371421:0.715757:0.355014:0.693153:0.355014:0.000000:0.000000:0.000000 f x+h f x:@0.747498:0.363103:0.822654:0.363103:0.822654:0.346697:0.747498:0.346697:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (:@0.752118:0.363103:0.756996:0.363103:0.756996:0.346670:0.752118:0.346670:0.000000 ) – ( ):@0.784643:0.363103:0.827459:0.363103:0.827459:0.346670:0.784643:0.346670:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 h:@0.782729:0.379496:0.792227:0.379496:0.792227:0.363090:0.782729:0.363090:0.000000 , tendremos :@0.834159:0.371424:0.930924:0.371424:0.930924:0.354990:0.834159:0.354990:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 que ´( ) = :@0.293667:0.390008:0.375929:0.390008:0.375929:0.373574:0.293667:0.373574:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x:@0.330003:0.390008:0.352312:0.390008:0.352312:0.373602:0.330003:0.373602:0.000000:0.000000:0.000000 (:@0.378362:0.384592:0.383240:0.384592:0.383240:0.368158:0.378362:0.368158:0.000000 sen x+h:@0.383166:0.384592:0.442456:0.384592:0.442456:0.368185:0.383166:0.368185:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (:@0.409875:0.384592:0.414753:0.384592:0.414753:0.368158:0.409875:0.368158:0.000000 ) – :@0.442401:0.384592:0.464324:0.384592:0.464324:0.368158:0.442401:0.368158:0.000000:0.000000:0.000000:0.000000 sen x:@0.464213:0.384592:0.498340:0.384592:0.498340:0.368185:0.464213:0.368185:0.000000:0.000000:0.000000:0.000000:0.000000 ):@0.498304:0.384592:0.503182:0.384592:0.503182:0.368158:0.498304:0.368158:0.000000 h:@0.436032:0.400984:0.445530:0.400984:0.445530:0.384578:0.436032:0.384578:0.000000 .:@0.505630:0.390000:0.512790:0.390000:0.512790:0.373566:0.505630:0.373566:0.000000:0.000000 f x:@0.293670:0.420205:0.315980:0.420205:0.315980:0.403799:0.293670:0.403799:0.000000:0.000000:0.000000 ´( )= :@0.298290:0.420205:0.335639:0.420205:0.335639:0.403771:0.298290:0.403771:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (:@0.367718:0.413896:0.372595:0.413896:0.372595:0.397462:0.367718:0.397462:0.000000 sen x cos h:@0.372522:0.413896:0.445403:0.413896:0.445403:0.397490:0.372522:0.397490:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 + :@0.445396:0.413896:0.464282:0.413896:0.464282:0.397462:0.445396:0.397462:0.000000:0.000000:0.000000 cos x sen h sen x:@0.464190:0.413896:0.588218:0.413896:0.588218:0.397490:0.464190:0.397490:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 – :@0.537064:0.413896:0.554183:0.413896:0.554183:0.397462:0.537064:0.397462:0.000000:0.000000:0.000000 ):@0.588181:0.413896:0.593059:0.413896:0.593059:0.397462:0.588181:0.397462:0.000000 h:@0.475639:0.430288:0.485137:0.430288:0.485137:0.413882:0.475639:0.413882:0.000000 :@0.625235:0.420206:0.923046:0.420206:0.923046:0.403773:0.625235:0.403773:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x:@0.293665:0.450855:0.315975:0.450855:0.315975:0.434449:0.293665:0.434449:0.000000:0.000000:0.000000 ´( )=:@0.298285:0.450855:0.331676:0.450855:0.331676:0.434421:0.298285:0.434421:0.000000:0.000000:0.000000:0.000000:0.000000 (:@0.353626:0.445439:0.358504:0.445439:0.358504:0.429005:0.353626:0.429005:0.000000 cos x sen h:@0.358430:0.445439:0.434552:0.445439:0.434552:0.429033:0.358430:0.429033:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ):@0.434563:0.445439:0.439441:0.445439:0.439441:0.429005:0.434563:0.429005:0.000000 h:@0.391784:0.461831:0.401282:0.461831:0.401282:0.445425:0.391784:0.445425:0.000000 – :@0.461382:0.450847:0.478501:0.450847:0.478501:0.434414:0.461382:0.434414:0.000000:0.000000:0.000000 sen x:@0.478409:0.450847:0.512536:0.450847:0.512536:0.434441:0.478409:0.434441:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.512499:0.450847:0.516530:0.450847:0.516530:0.434414:0.512499:0.434414:0.000000 1– :@0.539608:0.444095:0.561678:0.444095:0.561678:0.427661:0.539608:0.427661:0.000000:0.000000:0.000000 cos h:@0.561586:0.444095:0.597204:0.444095:0.597204:0.427689:0.561586:0.427689:0.000000:0.000000:0.000000:0.000000:0.000000 h:@0.563666:0.460487:0.573164:0.460487:0.573164:0.444081:0.563666:0.444081:0.000000 :@0.621262:0.450849:0.790572:0.450849:0.790572:0.434415:0.621262:0.434415:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x:@0.293668:0.478211:0.315978:0.478211:0.315978:0.461805:0.293668:0.461805:0.000000:0.000000:0.000000 ´( )= :@0.298289:0.478211:0.335637:0.478211:0.335637:0.461777:0.298289:0.461777:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cos x:@0.335545:0.478211:0.369090:0.478211:0.369090:0.461805:0.335545:0.461805:0.000000:0.000000:0.000000:0.000000:0.000000 (1) – :@0.369046:0.478211:0.408640:0.478211:0.408640:0.461777:0.369046:0.461777:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 sen x:@0.408511:0.478211:0.442638:0.478211:0.442638:0.461805:0.408511:0.461805:0.000000:0.000000:0.000000:0.000000:0.000000 (0) :@0.442602:0.478211:0.469180:0.478211:0.469180:0.461777:0.442602:0.461777:0.000000:0.000000:0.000000:0.000000:0.000000 f x:@0.293650:0.505573:0.315960:0.505573:0.315960:0.489167:0.293650:0.489167:0.000000:0.000000:0.000000 ´( )= :@0.298270:0.505573:0.335619:0.505573:0.335619:0.489139:0.298270:0.489139:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cos x:@0.335527:0.505573:0.369072:0.505573:0.369072:0.489167:0.335527:0.489167:0.000000:0.000000:0.000000:0.000000:0.000000 3.2 Derivada de la función coseno:@0.293632:0.536513:0.557975:0.536513:0.557975:0.519566:0.293632:0.519566:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 De forma similar, podemos hallar la derivada de :@0.293632:0.563875:0.637844:0.563875:0.637844:0.547441:0.293632:0.547441:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la función ( ) = :@0.293632:0.580516:0.413003:0.580516:0.413003:0.564083:0.293632:0.564083:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x:@0.369249:0.580516:0.389386:0.580516:0.389386:0.564110:0.369249:0.564110:0.000000:0.000000:0.000000:0.000000 cos x:@0.412892:0.580516:0.446438:0.580516:0.446438:0.564110:0.412892:0.564110:0.000000:0.000000:0.000000:0.000000:0.000000 .:@0.446393:0.580516:0.449596:0.580516:0.449596:0.564083:0.446393:0.564083:0.000000 f x:@0.293632:0.609820:0.315941:0.609820:0.315941:0.593414:0.293632:0.593414:0.000000:0.000000:0.000000 ´( ) = :@0.298252:0.609820:0.339558:0.609820:0.339558:0.593386:0.298252:0.593386:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (:@0.342613:0.604411:0.347491:0.604411:0.347491:0.587977:0.342613:0.587977:0.000000 cos x+h:@0.347418:0.604411:0.406118:0.604411:0.406118:0.588005:0.347418:0.588005:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (:@0.373538:0.604411:0.378415:0.604411:0.378415:0.587977:0.373538:0.587977:0.000000 ) – :@0.406063:0.604411:0.427986:0.604411:0.427986:0.587977:0.406063:0.587977:0.000000:0.000000:0.000000:0.000000 cos x:@0.427876:0.604411:0.461421:0.604411:0.461421:0.588005:0.427876:0.588005:0.000000:0.000000:0.000000:0.000000:0.000000 ):@0.461377:0.604411:0.466255:0.604411:0.466255:0.587977:0.461377:0.587977:0.000000 h:@0.399694:0.620803:0.409192:0.620803:0.409192:0.604397:0.399694:0.604397:0.000000 .:@0.469292:0.609820:0.476453:0.609820:0.476453:0.593386:0.469292:0.593386:0.000000:0.000000 f x:@0.293668:0.640025:0.315978:0.640025:0.315978:0.623619:0.293668:0.623619:0.000000:0.000000:0.000000 ´( ) = :@0.298289:0.640025:0.339595:0.640025:0.339595:0.623591:0.298289:0.623591:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (:@0.373141:0.633717:0.378019:0.633717:0.378019:0.617283:0.373141:0.617283:0.000000 cos x cos h cos x sen h cos x:@0.377945:0.633717:0.590704:0.633717:0.590704:0.617311:0.377945:0.617311:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 – :@0.450231:0.633717:0.467349:0.633717:0.467349:0.617283:0.450231:0.617283:0.000000:0.000000:0.000000 – :@0.540132:0.633717:0.557250:0.633717:0.557250:0.617283:0.540132:0.617283:0.000000:0.000000:0.000000 ):@0.590659:0.633717:0.595537:0.633717:0.595537:0.617283:0.590659:0.617283:0.000000 h:@0.479590:0.650109:0.489088:0.650109:0.489088:0.633703:0.479590:0.633703:0.000000 :@0.629186:0.640027:0.637414:0.640027:0.637414:0.623593:0.629186:0.623593:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 –:@0.293677:0.670676:0.302880:0.670676:0.302880:0.654242:0.293677:0.654242:0.000000 sen x :@0.302807:0.670676:0.343413:0.670676:0.343413:0.654270:0.302807:0.654270:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.343395:0.670676:0.347426:0.670676:0.347426:0.654242:0.343395:0.654242:0.000000 sen h:@0.356656:0.664197:0.392827:0.664197:0.392827:0.647791:0.356656:0.647791:0.000000:0.000000:0.000000:0.000000:0.000000 h:@0.370002:0.680589:0.379500:0.680589:0.379500:0.664183:0.370002:0.664183:0.000000 – :@0.402104:0.670673:0.419223:0.670673:0.419223:0.654240:0.402104:0.654240:0.000000:0.000000:0.000000 cos x:@0.419131:0.670673:0.452676:0.670673:0.452676:0.654267:0.419131:0.654267:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.452632:0.670673:0.456663:0.670673:0.456663:0.654240:0.452632:0.654240:0.000000 1– :@0.468179:0.663915:0.490250:0.663915:0.490250:0.647481:0.468179:0.647481:0.000000:0.000000:0.000000 cos h:@0.490158:0.663915:0.525776:0.663915:0.525776:0.647509:0.490158:0.647509:0.000000:0.000000:0.000000:0.000000:0.000000 h:@0.492238:0.680307:0.501736:0.680307:0.501736:0.663901:0.492238:0.663901:0.000000 f x:@0.293679:0.698030:0.315988:0.698030:0.315988:0.681624:0.293679:0.681624:0.000000:0.000000:0.000000 ´( ) = –:@0.298299:0.698030:0.348735:0.698030:0.348735:0.681597:0.298299:0.681597:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 sen x:@0.348624:0.698030:0.382751:0.698030:0.382751:0.681624:0.348624:0.681624:0.000000:0.000000:0.000000:0.000000:0.000000 (1) – :@0.382714:0.698030:0.422308:0.698030:0.422308:0.681597:0.382714:0.681597:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cos x:@0.422180:0.698030:0.455725:0.698030:0.455725:0.681624:0.422180:0.681624:0.000000:0.000000:0.000000:0.000000:0.000000 (0) :@0.455681:0.698030:0.486292:0.698030:0.486292:0.681597:0.455681:0.681597:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x:@0.293660:0.725392:0.315970:0.725392:0.315970:0.708986:0.293660:0.708986:0.000000:0.000000:0.000000 ´( ) = :@0.298280:0.725392:0.350962:0.725392:0.350962:0.708959:0.298280:0.708959:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.339476:0.725392:0.346931:0.725392:0.346931:0.708986:0.339476:0.708986:0.000000 Ejemplo 1. :@0.293623:0.756332:0.376971:0.756332:0.376971:0.739663:0.293623:0.739663:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Encuentra la derivada de la función ( ) = 5 :@0.376843:0.756332:0.689214:0.756332:0.689214:0.739898:0.376843:0.739898:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x:@0.635851:0.756332:0.652730:0.756332:0.652730:0.739926:0.635851:0.739926:0.000000:0.000000:0.000000 sen x :@0.689103:0.756332:0.726470:0.756332:0.726470:0.739926:0.689103:0.739926:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 – 4 :@0.726433:0.756332:0.752461:0.756332:0.752461:0.739898:0.726433:0.739898:0.000000:0.000000:0.000000:0.000000 cos x:@0.752350:0.756332:0.785896:0.756332:0.785896:0.739926:0.752350:0.739926:0.000000:0.000000:0.000000:0.000000:0.000000 . :@0.785852:0.756332:0.793086:0.756332:0.793086:0.739898:0.785852:0.739898:0.000000:0.000000 Solución: :@0.293586:0.783694:0.363968:0.783694:0.363968:0.767260:0.293586:0.767260:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x:@0.363829:0.783694:0.386138:0.783694:0.386138:0.767288:0.363829:0.767288:0.000000:0.000000:0.000000 ´( ) = 5 :@0.368449:0.783694:0.422621:0.783694:0.422621:0.767260:0.368449:0.767260:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cos x :@0.422511:0.783694:0.459296:0.783694:0.459296:0.767288:0.422511:0.767288:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 – 4 (– :@0.459252:0.783694:0.503171:0.783694:0.503171:0.767260:0.459252:0.767260:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 sen x:@0.503043:0.783694:0.537170:0.783694:0.537170:0.767288:0.503043:0.767288:0.000000:0.000000:0.000000:0.000000:0.000000 ) :@0.537133:0.783694:0.546042:0.783694:0.546042:0.767260:0.537133:0.767260:0.000000:0.000000 = 5 :@0.293550:0.803914:0.424241:0.803914:0.424241:0.787480:0.293550:0.787480:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cos x :@0.423965:0.803914:0.460750:0.803914:0.460750:0.787508:0.423965:0.787508:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 + 4 :@0.460706:0.803914:0.488501:0.803914:0.488501:0.787480:0.460706:0.787480:0.000000:0.000000:0.000000:0.000000 sen x:@0.488390:0.803914:0.522518:0.803914:0.522518:0.787508:0.488390:0.787508:0.000000:0.000000:0.000000:0.000000:0.000000 .:@0.522481:0.803914:0.525684:0.803914:0.525684:0.787480:0.522481:0.787480:0.000000 Ejemplo 2.:@0.293550:0.831276:0.373373:0.831276:0.373373:0.814606:0.293550:0.814606:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.373253:0.831276:0.377284:0.831276:0.377284:0.814842:0.373253:0.814842:0.000000 Encuentra la ecuación de la recta :@0.377524:0.831276:0.622583:0.831276:0.622583:0.814842:0.377524:0.814842:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tan:@0.622635:0.831276:0.646619:0.831276:0.646619:0.814870:0.622635:0.814870:0.000000:0.000000:0.000000 gente a la gráfica de ( ) = 2 :@0.646564:0.831276:0.852283:0.831276:0.852283:0.814842:0.646564:0.814842:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x:@0.798295:0.831276:0.815174:0.831276:0.815174:0.814870:0.798295:0.814870:0.000000:0.000000:0.000000 sen x:@0.852504:0.831276:0.886908:0.831276:0.886908:0.814870:0.852504:0.814870:0.000000:0.000000:0.000000:0.000000:0.000000 en el :@0.886852:0.831276:0.930827:0.831276:0.930827:0.814842:0.886852:0.814842:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 punto ( , 0).:@0.293513:0.847918:0.383211:0.847918:0.383211:0.831484:0.293513:0.831484:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.347023:0.847363:0.359300:0.847363:0.359300:0.833647:0.347023:0.833647:0.000000 Solución: :@0.293513:0.875280:0.363968:0.875280:0.363968:0.858846:0.293513:0.858846:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 La derivada ´( ) = 2 :@0.293513:0.895500:0.437126:0.895500:0.437126:0.879066:0.293513:0.879066:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x:@0.379420:0.895500:0.401655:0.895500:0.401655:0.879094:0.379420:0.879094:0.000000:0.000000:0.000000 cos x:@0.436611:0.895500:0.469744:0.895500:0.469744:0.879094:0.436611:0.879094:0.000000:0.000000:0.000000:0.000000:0.000000 nos proporciona la pendiente de la recta :@0.469652:0.895500:0.767675:0.895500:0.767675:0.879066:0.469652:0.879066:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tan:@0.767076:0.895500:0.791024:0.895500:0.791024:0.879094:0.767076:0.879094:0.000000:0.000000:0.000000 gente a la curva en :@0.790932:0.895500:0.930842:0.895500:0.930842:0.879066:0.790932:0.879066:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cualquier punto de abscisa , por lo :@0.293531:0.912141:0.553626:0.912141:0.553626:0.895708:0.293531:0.895708:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.492458:0.912141:0.499913:0.912141:0.499913:0.895735:0.492458:0.895735:0.000000 tan:@0.553497:0.912141:0.577482:0.912141:0.577482:0.895735:0.553497:0.895735:0.000000:0.000000:0.000000 to, la pendiente de la recta :@0.577426:0.912141:0.773944:0.912141:0.773944:0.895708:0.577426:0.895708:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tan:@0.773703:0.912141:0.797688:0.912141:0.797688:0.895735:0.773703:0.895735:0.000000:0.000000:0.000000 gente será::@0.797632:0.912141:0.877017:0.912141:0.877017:0.895708:0.797632:0.895708:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 m:@0.549466:0.939503:0.564081:0.939503:0.564081:0.923097:0.549466:0.923097:0.000000 = 2 :@0.564007:0.939503:0.595760:0.939503:0.595760:0.923070:0.564007:0.923070:0.000000:0.000000:0.000000:0.000000:0.000000 cos :@0.595650:0.939503:0.621814:0.939503:0.621814:0.923097:0.595650:0.923097:0.000000:0.000000:0.000000:0.000000 p:@0.621769:0.938949:0.634047:0.938949:0.634047:0.925233:0.621769:0.925233:0.000000 = –2:@0.633955:0.939503:0.670880:0.939503:0.670880:0.923070:0.633955:0.923070:0.000000:0.000000:0.000000:0.000000:0.000000 Tema 3. Derivadas de funciones trigonométricas:@0.073089:0.096721:0.787648:0.096721:0.787648:0.065479:0.073089:0.065479:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Encuentra la derivada de la función :@0.293660:0.167374:0.556950:0.167374:0.556950:0.150940:0.293660:0.150940:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f(x)=Sen(x):@0.556626:0.167374:0.631551:0.167374:0.631551:0.150968:0.556626:0.150968:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Reto matemático:@0.302768:0.139600:0.437491:0.139600:0.437491:0.122653:0.302768:0.122653:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 En la teoría de la música, el :@0.078581:0.321980:0.258825:0.321980:0.258825:0.307041:0.078581:0.307041:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 sonido puede modelarse :@0.078581:0.337109:0.247509:0.337109:0.247509:0.322170:0.078581:0.322170:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 como ondas sinusoidales. :@0.078581:0.352238:0.251387:0.352238:0.251387:0.337298:0.078581:0.337298:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 La función seno representa :@0.078581:0.367367:0.261019:0.367367:0.261019:0.352427:0.078581:0.352427:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la forma de onda de un :@0.078581:0.382496:0.236552:0.382496:0.236552:0.367556:0.078581:0.367556:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 sonido puro, y su derivada :@0.078581:0.397625:0.255339:0.397625:0.255339:0.382685:0.078581:0.382685:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 describe la rapidez de los :@0.078581:0.412754:0.248329:0.412754:0.248329:0.397814:0.078581:0.397814:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cambios en la presión del :@0.078581:0.427883:0.250647:0.427883:0.250647:0.412943:0.078581:0.412943:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 aire, lo cual es esencial para :@0.078581:0.443012:0.262541:0.443012:0.262541:0.428072:0.078581:0.428072:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 entender la acústica y el :@0.078581:0.458141:0.240774:0.458141:0.240774:0.443201:0.078581:0.443201:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 diseño de instrumentos :@0.078581:0.473270:0.238918:0.473270:0.238918:0.458330:0.078581:0.458330:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 musicales. En el contexto :@0.078581:0.488399:0.247951:0.488399:0.247951:0.473459:0.078581:0.473459:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 del sonido, la derivada :@0.078581:0.503528:0.229524:0.503528:0.229524:0.488588:0.078581:0.488588:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 está relacionada con la :@0.078581:0.518657:0.232511:0.518657:0.232511:0.503717:0.078581:0.503717:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 velocidad de cambio :@0.078581:0.533786:0.225668:0.533786:0.225668:0.518631:0.078581:0.518631:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de :@0.225521:0.533786:0.246338:0.533786:0.246338:0.518846:0.225521:0.518846:0.000000:0.000000:0.000000 la presión, lo que influye :@0.078581:0.548915:0.242159:0.548915:0.242159:0.533975:0.078581:0.533975:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 en la percepción del :@0.078581:0.564043:0.216712:0.564043:0.216712:0.549104:0.078581:0.549104:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 sonido, fundamental para :@0.078581:0.579172:0.251669:0.579172:0.251669:0.564233:0.078581:0.564233:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la percepción y emisión de :@0.078581:0.594301:0.259636:0.594301:0.259636:0.579362:0.078581:0.579362:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 un sonido.:@0.078581:0.609430:0.147719:0.609430:0.147719:0.594490:0.078581:0.594490:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Interdisciplinariedad :@0.078581:0.257370:0.244955:0.257370:0.244955:0.240423:0.078581:0.240423:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Matemática y :@0.078581:0.274012:0.180782:0.274012:0.180782:0.257578:0.078581:0.257578:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 música:@0.078581:0.290653:0.130342:0.290653:0.130342:0.274220:0.078581:0.274220:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 -10:@0.700634:0.664726:0.713299:0.664726:0.713299:0.656122:0.700634:0.656122:0.000000:0.000000:0.000000 10:@0.889318:0.663953:0.899065:0.663953:0.899065:0.655349:0.889318:0.655349:0.000000:0.000000 0:@0.806662:0.663366:0.811536:0.663366:0.811536:0.654762:0.806662:0.654762:0.000000 1:@0.806662:0.602059:0.811536:0.602059:0.811536:0.593455:0.806662:0.593455:0.000000 -1:@0.806662:0.705110:0.814452:0.705110:0.814452:0.696507:0.806662:0.696507:0.000000:0.000000 h:@0.881057:0.670267:0.887399:0.670267:0.887399:0.659503:0.881057:0.659503:0.000000 f h:@0.861644:0.573109:0.872976:0.573109:0.872976:0.563781:0.861644:0.563781:0.000000:0.000000:0.000000 ( )=:@0.864557:0.573109:0.882033:0.573109:0.882033:0.563788:0.864557:0.563788:0.000000:0.000000:0.000000:0.000000 1 :@0.885883:0.568811:0.893345:0.568811:0.893345:0.559490:0.885883:0.559490:0.000000:0.000000 - cos h:@0.893345:0.568811:0.919220:0.568811:0.919220:0.559483:0.893345:0.559483:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 h:@0.900200:0.577589:0.905696:0.577589:0.905696:0.568261:0.900200:0.568261:0.000000 f h:@0.864640:0.598782:0.875972:0.598782:0.875972:0.589453:0.864640:0.589453:0.000000:0.000000:0.000000 ( )=:@0.867553:0.598782:0.885029:0.598782:0.885029:0.589461:0.867553:0.589461:0.000000:0.000000:0.000000:0.000000 sen h:@0.888880:0.594491:0.910247:0.594491:0.910247:0.585163:0.888880:0.585163:0.000000:0.000000:0.000000:0.000000:0.000000 h:@0.897660:0.603269:0.903156:0.603269:0.903156:0.593941:0.897660:0.593941:0.000000 f h:@0.780932:0.573773:0.794007:0.573773:0.794007:0.563009:0.780932:0.563009:0.000000:0.000000:0.000000 ( ):@0.784293:0.573773:0.797380:0.573773:0.797380:0.563018:0.784293:0.563018:0.000000:0.000000:0.000000 p:@0.838637:0.723853:0.850105:0.723853:0.850105:0.713801:0.838637:0.713801:0.000000 :@0.849870:0.724512:0.852802:0.724512:0.852802:0.712560:0.849870:0.712560:0.000000 Figura 3.1:@0.852749:0.724512:0.903587:0.724512:0.903587:0.712560:0.852749:0.712560:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 DBA 8 (Ev. 1) Utiliza la derivada para estudiar la variación y relaciona características de la derivada con características de la función.:@0.234596:0.971366:0.915450:0.971366:0.915450:0.959414:0.234596:0.959414:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x:@0.744288:0.184347:0.760704:0.184347:0.760704:0.170924:0.744288:0.170924:0.000000:0.000000:0.000000 '( ) = cos( ) y '(0) = 1:@0.748068:0.184347:0.871293:0.184347:0.871293:0.170902:0.748068:0.170902:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.804018:0.184347:0.810117:0.184347:0.810117:0.170924:0.804018:0.170924:0.000000 f:@0.827000:0.184347:0.830841:0.184347:0.830841:0.170924:0.827000:0.170924:0.000000 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