145:@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
Ejercicio 3::@0.073089:0.136836:0.153229:0.136836:0.153229:0.120167:0.073089:0.120167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
  ( ) = 2  :@0.153105:0.136836:0.225378:0.136836:0.225378:0.120402:0.153105:0.120402:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.157063:0.136836:0.173942:0.136836:0.173942:0.120430:0.157063:0.120430:0.000000:0.000000:0.000000
3 4:@0.206363:0.130772:0.216794:0.129511:0.216794:0.119930:0.206363:0.121191:0.000000:0.000000:0.000000
x:@0.216751:0.126989:0.221355:0.126989:0.221355:0.117408:0.216751:0.117408:0.000000
Solución :@0.073094:0.164198:0.140347:0.164198:0.140347:0.147764:0.073094:0.147764:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f´ x:@0.140226:0.164198:0.163953:0.164198:0.163953:0.147792:0.140226:0.147792:0.000000:0.000000:0.000000:0.000000
( ) = 2:@0.151693:0.164198:0.196478:0.164198:0.196478:0.147764:0.151693:0.147764:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3 4:@0.196353:0.158135:0.206784:0.156874:0.206784:0.147293:0.196353:0.148555:0.000000:0.000000:0.000000
x :@0.206741:0.154352:0.213652:0.154352:0.213652:0.144771:0.206741:0.144771:0.000000:0.000000
?:@0.213594:0.163645:0.219723:0.163645:0.219723:0.149929:0.213594:0.149929:0.000000
  3 4:@0.219631:0.164199:0.263196:0.164199:0.263196:0.147766:0.219631:0.147766:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.223589:0.164782:0.227675:0.164782:0.227675:0.147128:0.223589:0.147128:0.000000
4:@0.236477:0.156875:0.241714:0.156875:0.241714:0.147294:0.236477:0.147294:0.000000
x:@0.241671:0.154352:0.246275:0.154352:0.246275:0.144771:0.241671:0.144771:0.000000
63:@0.246225:0.164782:0.254305:0.164782:0.254305:0.147128:0.246225:0.147128:0.000000:0.000000
x:@0.263116:0.158135:0.267462:0.158135:0.267462:0.148571:0.263116:0.148571:0.000000
?:@0.267423:0.163645:0.273553:0.163645:0.273553:0.149929:0.267423:0.149929:0.000000
ln:@0.273461:0.164199:0.286677:0.164199:0.286677:0.147793:0.273461:0.147793:0.000000:0.000000
4 ( 3):@0.286622:0.164199:0.335788:0.164199:0.335788:0.147766:0.286622:0.147766:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4 :@0.295531:0.164782:0.304127:0.164782:0.304127:0.147128:0.295531:0.147128:0.000000:0.000000
ln:@0.308839:0.164199:0.322056:0.164199:0.322056:0.147793:0.308839:0.147793:0.000000:0.000000
?:@0.335696:0.163645:0.341825:0.163645:0.341825:0.149929:0.335696:0.149929:0.000000
ln:@0.341733:0.164199:0.354950:0.164199:0.354950:0.147793:0.341733:0.147793:0.000000:0.000000
2:@0.354894:0.164199:0.363877:0.164199:0.363877:0.147766:0.354894:0.147766:0.000000
Escribimos la función de manera más clara::@0.073116:0.195139:0.409665:0.195139:0.409665:0.178192:0.073116:0.178192:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Sea:   = 3  y  ( ) = 2:@0.409490:0.195139:0.561427:0.195137:0.561427:0.178703:0.409490:0.178706:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u :@0.450133:0.195139:0.462687:0.195139:0.462687:0.178733:0.450133:0.178733:0.000000:0.000000
3x:@0.486352:0.189073:0.496150:0.189073:0.496150:0.179492:0.486352:0.179492:0.000000:0.000000
f x:@0.512022:0.195137:0.528901:0.195137:0.528901:0.178731:0.512022:0.178731:0.000000:0.000000:0.000000
u:@0.561323:0.189073:0.567022:0.189073:0.567022:0.179492:0.561323:0.179492:0.000000
Derivamos cada parte usando la regla de la cadena:  :@0.073089:0.218926:0.483780:0.218926:0.483780:0.201979:0.073089:0.201979:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a.  La derivada de  ( ) = 2  respecto a   es:  '( ) = 2   ln(2)∙ :@0.104633:0.247873:0.527504:0.247873:0.527504:0.231439:0.104633:0.231439:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.244652:0.247873:0.261531:0.247873:0.261531:0.231466:0.244652:0.231466:0.000000:0.000000:0.000000
u:@0.293961:0.241809:0.299660:0.241809:0.299660:0.232228:0.293961:0.232228:0.000000
u:@0.382980:0.247873:0.392295:0.247873:0.392295:0.231466:0.382980:0.231466:0.000000
f  x:@0.418875:0.247873:0.442197:0.247873:0.442197:0.231466:0.418875:0.231466:0.000000:0.000000:0.000000:0.000000
u:@0.474639:0.241809:0.480337:0.241809:0.480337:0.232228:0.474639:0.232228:0.000000
du:@0.530851:0.239248:0.549350:0.239248:0.549350:0.222842:0.530851:0.222842:0.000000:0.000000
dx:@0.531771:0.255640:0.548411:0.255640:0.548411:0.239234:0.531771:0.239234:0.000000:0.000000
b.  Ahora derivamos  ( ) = 3  respecto a   es: :@0.104633:0.277893:0.439143:0.277893:0.439143:0.261460:0.104633:0.261460:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.262580:0.277893:0.279460:0.277893:0.279460:0.261487:0.262580:0.261487:0.000000:0.000000:0.000000
4 x:@0.311883:0.271830:0.321681:0.270568:0.321681:0.260987:0.311883:0.262249:0.000000:0.000000:0.000000
x:@0.404997:0.277893:0.412452:0.277893:0.412452:0.261487:0.404997:0.261487:0.000000
du:@0.442533:0.271055:0.461032:0.271055:0.461032:0.254649:0.442533:0.254649:0.000000:0.000000
dx:@0.443453:0.287447:0.460093:0.287447:0.460093:0.271041:0.443453:0.271041:0.000000:0.000000
 = 3   ln(3)∙ :@0.464438:0.277892:0.549096:0.277893:0.549096:0.261460:0.464438:0.261458:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4 x:@0.492136:0.271830:0.501933:0.270568:0.501933:0.260987:0.492136:0.262249:0.000000:0.000000:0.000000
d:@0.557068:0.269267:0.566327:0.269267:0.566327:0.252861:0.557068:0.252861:0.000000
dx:@0.553368:0.285660:0.570008:0.285660:0.570008:0.269254:0.553368:0.269254:0.000000:0.000000
 (4 ):@0.574352:0.277893:0.601438:0.277893:0.601438:0.261460:0.574352:0.261460:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.592003:0.271830:0.596607:0.271830:0.596607:0.262249:0.592003:0.262249:0.000000
c.  Derivamos 4  respecto a x: :@0.104633:0.306125:0.328702:0.306125:0.328702:0.289691:0.104633:0.289691:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.225726:0.300061:0.230329:0.300061:0.230329:0.290480:0.225726:0.290480:0.000000
d:@0.336654:0.299287:0.345913:0.299287:0.345913:0.282881:0.336654:0.282881:0.000000
dx:@0.332955:0.315679:0.349595:0.315679:0.349595:0.299273:0.332955:0.299273:0.000000:0.000000
 (4 ) = 4  ln(4):@0.353939:0.306124:0.449364:0.306125:0.449364:0.289691:0.353939:0.289690:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.371590:0.300061:0.376194:0.300061:0.376194:0.290480:0.371590:0.290480:0.000000
x:@0.408637:0.300061:0.413241:0.300061:0.413241:0.290480:0.408637:0.290480:0.000000
d.  Por lo tanto, tenemos: :@0.104633:0.335252:0.297377:0.335252:0.297377:0.318818:0.104633:0.318818:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
du:@0.300657:0.327520:0.319156:0.327520:0.319156:0.311114:0.300657:0.311114:0.000000:0.000000
dx:@0.301577:0.343912:0.318217:0.343912:0.318217:0.327506:0.301577:0.327506:0.000000:0.000000
 = 3  (3) ∙ 4   ln(4):@0.322561:0.335259:0.447063:0.335252:0.447063:0.318818:0.322561:0.318825:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4 x:@0.350259:0.329188:0.360057:0.327927:0.360057:0.318346:0.350259:0.319607:0.000000:0.000000:0.000000
x:@0.402378:0.329188:0.406982:0.329188:0.406982:0.319607:0.402378:0.319607:0.000000
Sustituimos en la derivada de f(x): :@0.073083:0.369756:0.342416:0.369756:0.342416:0.352809:0.073083:0.352809:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Respuesta:   '( ) = 2 :@0.073083:0.393540:0.214892:0.393540:0.214892:0.377106:0.073083:0.377106:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.154387:0.393540:0.178409:0.393540:0.178409:0.377134:0.154387:0.377134:0.000000:0.000000:0.000000
3  4  x:@0.214788:0.387488:0.234373:0.384965:0.234373:0.375384:0.214788:0.377907:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
   ln(2) ∙ 3  ln(3) ∙ 4   ln(4):@0.234330:0.393552:0.417349:0.393552:0.417349:0.377118:0.234330:0.377118:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n :@0.278287:0.393552:0.291025:0.393552:0.291025:0.377146:0.278287:0.377146:0.000000:0.000000
4 x:@0.306938:0.387488:0.316736:0.386226:0.316736:0.376646:0.306938:0.377907:0.000000:0.000000:0.000000
x:@0.372664:0.387488:0.377268:0.387488:0.377268:0.377907:0.372664:0.377907:0.000000
Ejercicio 4::@0.073096:0.428056:0.153238:0.428056:0.153238:0.411386:0.073096:0.411386:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.174050:0.480561:0.178081:0.480561:0.178081:0.464127:0.174050:0.464127:0.000000
Apliquemos logaritmo natural a ambos lados de la función y utilicemos las propiedades :@0.073086:0.511501:0.710827:0.511501:0.710827:0.495067:0.073086:0.495067:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de logaritmos.:@0.073086:0.528142:0.176980:0.528142:0.176980:0.511709:0.073086:0.511709:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Usemos derivación implícita:@0.073089:0.602298:0.277954:0.602298:0.277954:0.585864:0.073089:0.585864:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La derivada ya terminó. Simplifiquémosla sustituyendo y por la expresión en función de :@0.073089:0.688424:0.710782:0.688424:0.710782:0.671990:0.073089:0.671990:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y simplificando para que quede de la forma explícita::@0.073089:0.705065:0.467137:0.705065:0.467137:0.688632:0.073089:0.688632:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.373685:0.762106:0.377587:0.762106:0.377587:0.745437:0.373685:0.745437:0.000000
 :@0.333629:0.821578:0.337531:0.821578:0.337531:0.804909:0.333629:0.804909:0.000000
 :@0.273513:0.881638:0.277415:0.881638:0.277415:0.864968:0.273513:0.864968:0.000000
Esta derivada se puede resolver al emplear la regla de la cadena o con :@0.197604:0.437032:0.710817:0.437032:0.710817:0.420598:0.197604:0.420598:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
logaritmos. Utilizaremos logaritmos, porque generalmente simplifica el :@0.197604:0.453674:0.710784:0.453674:0.710784:0.437240:0.197604:0.437240:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
trabajo y en otras derivadas es imperativo su uso cuando lo que se va a :@0.197604:0.470316:0.710673:0.470316:0.710673:0.453882:0.197604:0.453882:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
derivar no es exponencial ni polinómico. :@0.197604:0.486958:0.495437:0.486958:0.495437:0.470524:0.197604:0.470524:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Las derivadas de :@0.740630:0.201471:0.853042:0.201471:0.853042:0.186531:0.740630:0.186531:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
funciones exponenciales :@0.740630:0.216600:0.907868:0.216600:0.907868:0.201660:0.740630:0.201660:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
muestran cómo cambian :@0.740630:0.231729:0.910947:0.231729:0.910947:0.216789:0.740630:0.216789:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
fenómenos que crecen :@0.740630:0.246858:0.897348:0.246858:0.897348:0.231918:0.740630:0.231918:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
o decrecen rápido, como :@0.740630:0.261987:0.909662:0.261987:0.909662:0.247047:0.740630:0.247047:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
poblaciones, intereses o :@0.740630:0.277116:0.902527:0.277116:0.902527:0.262176:0.740630:0.262176:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
descomposición radiactiva.:@0.740630:0.292244:0.919977:0.292244:0.919977:0.277305:0.740630:0.277305:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Por ejemplo, :@0.740630:0.307373:0.826830:0.307373:0.826830:0.292434:0.740630:0.292434:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.740630:0.328806:0.744295:0.328806:0.744295:0.313866:0.740630:0.313866:0.000000
d:@0.752329:0.323177:0.761588:0.323177:0.761588:0.306771:0.752329:0.306771:0.000000
dx:@0.748629:0.339569:0.765269:0.339569:0.765269:0.323163:0.748629:0.323163:0.000000:0.000000
 e  = e , lo que hace :@0.769615:0.328806:0.902092:0.328806:0.902092:0.313866:0.769615:0.313866:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.781248:0.323293:0.785434:0.323293:0.785434:0.314584:0.781248:0.314584:0.000000
x:@0.810516:0.323293:0.814701:0.323293:0.814701:0.314584:0.810516:0.314584:0.000000
a e  clave en modelos de :@0.740627:0.350239:0.907863:0.350239:0.907863:0.335299:0.740627:0.335299:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.759789:0.344726:0.763974:0.344726:0.763974:0.336016:0.759789:0.336016:0.000000
cambio proporcional.:@0.740637:0.365368:0.881902:0.365368:0.881902:0.350428:0.740637:0.350428:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejemplos claros de su uso :@0.740637:0.380497:0.913357:0.380497:0.913357:0.365557:0.740637:0.365557:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en estas ciencias: biología, :@0.740637:0.395626:0.916754:0.395626:0.916754:0.380686:0.740637:0.380686:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
economía y física, se usan :@0.740637:0.410755:0.913447:0.410755:0.913447:0.395815:0.740637:0.395815:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
para describir fenómenos :@0.740637:0.425883:0.912646:0.425883:0.912646:0.410944:0.740637:0.410944:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
como el crecimiento :@0.740637:0.441012:0.880602:0.441012:0.880602:0.426073:0.740637:0.426073:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
poblacional o la :@0.740637:0.456141:0.849173:0.456141:0.849173:0.441202:0.740637:0.441202:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
descomposición radiactiva.:@0.740637:0.471270:0.919984:0.471270:0.919984:0.456330:0.740637:0.456330:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Interdisciplinaria :@0.739817:0.141157:0.863226:0.141157:0.863226:0.125750:0.739817:0.125750:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Matemática  :@0.739817:0.156286:0.825310:0.156286:0.825310:0.141346:0.739817:0.141346:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y otras disciplinas:@0.739817:0.171415:0.855046:0.171415:0.855046:0.156475:0.739817:0.156475:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
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