138:@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
Como su nombre lo sugiere, la derivación implícita permite encontrar la derivada de :@0.293660:0.348880:0.931044:0.348880:0.931044:0.332446:0.293660:0.332446:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
funciones implícitas y es útil para resolver diversos problemas de física, economía e :@0.293660:0.365521:0.930347:0.365521:0.930347:0.349088:0.293660:0.349088:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ingeniería que involucran ecuaciones precisamente implícitas.:@0.293660:0.382163:0.743692:0.382163:0.743692:0.365730:0.293660:0.365730:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En las secciones anteriores hemos trabajado mayoritariamente las funciones de la forma :@0.293660:0.409525:0.931420:0.409525:0.931420:0.393091:0.293660:0.393091:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y=f(x):@0.293660:0.426167:0.333733:0.426167:0.333733:0.409761:0.293660:0.409761:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
, en donde la variable y está explícitamente expresada en función de la variable x. :@0.333659:0.426167:0.930658:0.426167:0.930658:0.409733:0.333659:0.409733:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Cuando la función está expresada en términos de las variables   e   por medio de una :@0.293660:0.442809:0.930864:0.442809:0.930864:0.426375:0.293660:0.426375:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.756271:0.442809:0.789036:0.442809:0.789036:0.426403:0.756271:0.426403:0.000000:0.000000:0.000000
ecuación de la forma  ( ,  ) = 0 (en algunos casos no se puede despejar la variable  ), :@0.293660:0.459451:0.930943:0.459451:0.930943:0.443017:0.293660:0.443017:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x y:@0.455423:0.459451:0.488151:0.459451:0.488151:0.443045:0.455423:0.443045:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.911242:0.459451:0.918715:0.459451:0.918715:0.443045:0.911242:0.443045:0.000000
hablamos de una función implícita. :@0.293660:0.476093:0.553018:0.476093:0.553018:0.459659:0.293660:0.459659:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Función explícita   =  ( ) , por ejemplo  = 3 – 5 + 10.:@0.293660:0.503455:0.690052:0.503457:0.690052:0.487023:0.293660:0.487021:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.420247:0.503455:0.427720:0.503455:0.427720:0.487048:0.420247:0.487048:0.000000
f x:@0.446440:0.503455:0.463320:0.503455:0.463320:0.487048:0.446440:0.487048:0.000000:0.000000:0.000000
y :@0.572272:0.503455:0.582985:0.503455:0.582985:0.487048:0.572272:0.487048:0.000000:0.000000
x:@0.606675:0.503455:0.614130:0.503455:0.614130:0.487048:0.606675:0.487048:0.000000
2 :@0.614065:0.497393:0.621609:0.497393:0.621609:0.487812:0.614065:0.487812:0.000000:0.000000
x :@0.643537:0.503457:0.654231:0.503457:0.654231:0.487051:0.643537:0.487051:0.000000:0.000000
Función implícita  ( ,  ) = 0, por ejemplo  +  – x – 8 = 0.:@0.293670:0.530819:0.708816:0.530820:0.708816:0.514386:0.293670:0.514385:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x y:@0.422355:0.530819:0.453703:0.530819:0.453703:0.514413:0.422355:0.514413:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.586401:0.530819:0.593856:0.530819:0.593856:0.514413:0.586401:0.514413:0.000000
2 :@0.593792:0.524756:0.601336:0.524756:0.601336:0.515175:0.593792:0.515175:0.000000:0.000000
y:@0.616122:0.530820:0.623595:0.530820:0.623595:0.514414:0.616122:0.514414:0.000000
3 :@0.623533:0.524756:0.631077:0.524756:0.631077:0.515175:0.623533:0.515175:0.000000:0.000000
Tema 5. Derivación implícita:@0.073089:0.098522:0.492168:0.098522:0.492168:0.067281:0.073089:0.067281:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Un carrito en una montaña rusa sigue una trayectoria circular. La relación entre su :@0.293660:0.167374:0.919941:0.167374:0.919941:0.150940:0.293660:0.150940:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
posición  (horizontal) y   (vertical) en el plano está dada por la ecuación del círculo: :@0.293660:0.184016:0.920035:0.184016:0.920035:0.167582:0.293660:0.167582:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 x:@0.356282:0.184016:0.367528:0.184016:0.367528:0.167610:0.356282:0.167610:0.000000:0.000000
y:@0.473536:0.184016:0.481009:0.184016:0.481009:0.167610:0.473536:0.167610:0.000000
 :@0.915844:0.184016:0.919875:0.184016:0.919875:0.167582:0.915844:0.167582:0.000000
x:@0.293660:0.200658:0.301115:0.200658:0.301115:0.184252:0.293660:0.184252:0.000000
2 :@0.301048:0.194594:0.308592:0.194594:0.308592:0.185013:0.301048:0.185013:0.000000:0.000000
+   = 25.:@0.308542:0.200658:0.375812:0.200658:0.375812:0.184224:0.308542:0.184224:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.323378:0.200658:0.330851:0.200658:0.330851:0.184252:0.323378:0.184252:0.000000
2:@0.330789:0.194594:0.336026:0.194594:0.336026:0.185013:0.330789:0.185013:0.000000
Encuentra la derivada de   respecto a   (:@0.293660:0.230502:0.584053:0.230502:0.584053:0.214068:0.293660:0.214068:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.477070:0.230502:0.484543:0.230502:0.484543:0.214096:0.477070:0.214096:0.000000
x:@0.567836:0.230502:0.575291:0.230502:0.575291:0.214096:0.567836:0.214096:0.000000
dy:@0.590726:0.223292:0.605871:0.223292:0.605871:0.208377:0.590726:0.208377:0.000000:0.000000
dx:@0.590743:0.239681:0.605871:0.239681:0.605871:0.224767:0.590743:0.224767:0.000000:0.000000
) usando derivación implícita.:@0.612544:0.230498:0.824920:0.230498:0.824920:0.214064:0.612544:0.214064:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Qué indica esta derivada sobre la pendiente de la trayectoria en cualquier punto ( ,  ) :@0.293657:0.257860:0.919853:0.257860:0.919853:0.241426:0.293657:0.241426:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.889168:0.257860:0.911018:0.257860:0.911018:0.241454:0.889168:0.241454:0.000000:0.000000:0.000000
de la curva? :@0.293638:0.274502:0.383771:0.274502:0.383771:0.258068:0.293638:0.258068:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
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 las figuras 5.1 y 5.2 podemos observar que ambas funciones son derivables.:@0.293660:0.818830:0.861870:0.818830:0.861870:0.802396:0.293660:0.802396:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Cuando   se define como función implícita de  , la derivada implícita de   con respecto :@0.293660:0.846192:0.930952:0.846192:0.930952:0.829758:0.293660:0.829758:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.355527:0.846192:0.363000:0.846192:0.363000:0.829786:0.355527:0.829786:0.000000
x:@0.632906:0.846192:0.640361:0.846192:0.640361:0.829786:0.632906:0.829786:0.000000
y:@0.820163:0.846192:0.827636:0.846192:0.827636:0.829786:0.820163:0.829786:0.000000
a   se nota como :@0.293623:0.867105:0.420762:0.867105:0.420762:0.850671:0.293623:0.850671:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.305846:0.867105:0.313301:0.867105:0.313301:0.850699:0.305846:0.850699:0.000000
dy:@0.426629:0.859368:0.443288:0.859368:0.443288:0.842962:0.426629:0.842962:0.000000:0.000000
dx:@0.426629:0.875760:0.443269:0.875760:0.443269:0.859354:0.426629:0.859354:0.000000:0.000000
 o como  ´. :@0.449196:0.867106:0.533391:0.867106:0.533391:0.850673:0.449196:0.850673:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.513309:0.867106:0.520782:0.867106:0.520782:0.850700:0.513309:0.850700:0.000000
Figura 5.1:@0.309062:0.773274:0.378965:0.773274:0.378965:0.756840:0.309062:0.756840:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Figura 5.2:@0.630434:0.773871:0.700338:0.773871:0.700338:0.757437:0.630434:0.757437:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En situaciones donde los :@0.079392:0.415897:0.246746:0.415897:0.246746:0.400957:0.079392:0.400957:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
objetos se mueven a lo :@0.079392:0.431026:0.236052:0.431026:0.236052:0.416086:0.079392:0.416086:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
largo de trayectorias no :@0.079392:0.446155:0.238478:0.446155:0.238478:0.431215:0.079392:0.431215:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
lineales, como en el caso :@0.079392:0.461284:0.246390:0.461284:0.246390:0.446344:0.079392:0.446344:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de un proyectil o un objeto :@0.079392:0.476413:0.262695:0.476413:0.262695:0.461473:0.079392:0.461473:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en una pista curva (por :@0.079392:0.491542:0.234977:0.491542:0.234977:0.476602:0.079392:0.476602:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ejemplo, una montaña :@0.079392:0.506671:0.233289:0.506671:0.233289:0.491731:0.079392:0.491731:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
rusa), la derivación :@0.079392:0.521800:0.205024:0.521800:0.205024:0.506860:0.079392:0.506860:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
implícita se utiliza para :@0.079392:0.536929:0.232323:0.536929:0.232323:0.521989:0.079392:0.521989:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
calcular la velocidad y la :@0.079392:0.552058:0.241505:0.552058:0.241505:0.537118:0.079392:0.537118:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
aceleración en diferentes :@0.079392:0.567186:0.248167:0.567186:0.248167:0.552247:0.079392:0.552247:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
puntos de su trayectoria.:@0.079392:0.582315:0.242041:0.582315:0.242041:0.567376:0.079392:0.567376:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La relación entre las :@0.079392:0.602803:0.213150:0.602803:0.213150:0.587863:0.079392:0.587863:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
coordenadas   e   puede :@0.079392:0.617931:0.248036:0.617931:0.248036:0.602992:0.079392:0.602992:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.168919:0.617931:0.197651:0.617931:0.197651:0.603017:0.168919:0.603017:0.000000:0.000000:0.000000
estar representada por una :@0.079376:0.633060:0.260707:0.633060:0.260707:0.618121:0.079376:0.618121:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ecuación como::@0.079376:0.648189:0.184950:0.648189:0.184950:0.633250:0.079376:0.633250:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.079376:0.668676:0.086153:0.668676:0.086153:0.653762:0.079376:0.653762:0.000000
2:@0.086109:0.663169:0.090870:0.663169:0.090870:0.654459:0.086109:0.654459:0.000000
 +   = :@0.090827:0.668682:0.136531:0.668682:0.136531:0.653742:0.090827:0.653742:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.107913:0.668682:0.114707:0.668682:0.114707:0.653767:0.107913:0.653767:0.000000
2:@0.114644:0.663169:0.119404:0.663169:0.119404:0.654459:0.114644:0.654459:0.000000
r:@0.136447:0.668682:0.141250:0.668682:0.141250:0.653767:0.136447:0.653767:0.000000
2:@0.141186:0.663169:0.145947:0.663169:0.145947:0.654459:0.141186:0.654459:0.000000
donde r es el radio de la :@0.079392:0.689171:0.240990:0.689171:0.240990:0.674231:0.079392:0.674231:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
curva. Al usar la derivación :@0.079392:0.704300:0.257662:0.704300:0.257662:0.689360:0.079392:0.689360:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
implícita, se puede :@0.079392:0.719429:0.207122:0.719429:0.207122:0.704489:0.079392:0.704489:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
calcular la velocidad y la :@0.079392:0.734558:0.241505:0.734558:0.241505:0.719618:0.079392:0.719618:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
aceleración del carrito en :@0.079392:0.749687:0.249055:0.749687:0.249055:0.734747:0.079392:0.734747:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
diferentes puntos de la :@0.079392:0.764816:0.234341:0.764816:0.234341:0.749876:0.079392:0.749876:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
curva: 2  + 2  :@0.079392:0.783689:0.172767:0.783689:0.172767:0.768749:0.079392:0.768749:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.130498:0.783689:0.137275:0.783689:0.137275:0.768775:0.130498:0.768775:0.000000
y:@0.162376:0.783689:0.169170:0.783689:0.169170:0.768775:0.162376:0.768775:0.000000
dy:@0.179462:0.776793:0.194606:0.776793:0.194606:0.761878:0.179462:0.761878:0.000000:0.000000
dx:@0.179462:0.793183:0.194589:0.793183:0.194589:0.778268:0.179462:0.778268:0.000000:0.000000
 = 0:@0.201282:0.783689:0.226551:0.783689:0.226551:0.768749:0.201282:0.768749:0.000000:0.000000:0.000000:0.000000
Interdisciplinaria :@0.078573:0.355578:0.201982:0.355578:0.201982:0.340172:0.078573:0.340172:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Matemática  :@0.078573:0.370707:0.164066:0.370707:0.164066:0.355767:0.078573:0.355767:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y física:@0.078573:0.385836:0.121813:0.385836:0.121813:0.370896:0.078573:0.370896:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.563981:0.679071:0.570461:0.679071:0.570461:0.665751:0.563981:0.665751:0.000000
y:@0.397982:0.581884:0.404463:0.581884:0.404463:0.568565:0.397982:0.568565:0.000000
5:@0.526634:0.672992:0.532665:0.672992:0.532665:0.662346:0.526634:0.662346:0.000000
0:@0.411082:0.672992:0.417113:0.672992:0.417113:0.662346:0.411082:0.662346:0.000000
5:@0.310814:0.672992:0.316844:0.672992:0.316844:0.662346:0.310814:0.662346:0.000000
(1, 2):@0.431268:0.611098:0.454933:0.611098:0.454933:0.600452:0.431268:0.600452:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.779126:0.689383:0.785351:0.689383:0.785351:0.678394:0.779126:0.678394:0.000000
x:@0.887629:0.698216:0.894317:0.698216:0.894317:0.684469:0.887629:0.684469:0.000000
y:@0.663411:0.581910:0.670100:0.581910:0.670100:0.568163:0.663411:0.568163:0.000000
-2:@0.678644:0.720442:0.688594:0.720442:0.688594:0.709454:0.678644:0.709454:0.000000:0.000000
2:@0.681241:0.640735:0.687466:0.640735:0.687466:0.629747:0.681241:0.629747:0.000000
4:@0.679809:0.601809:0.686034:0.601809:0.686034:0.590821:0.679809:0.590821:0.000000
4:@0.857462:0.689379:0.863686:0.689379:0.863686:0.678390:0.857462:0.678390:0.000000
(2, 1):@0.737446:0.656794:0.770148:0.656794:0.770148:0.642082:0.737446:0.642082:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
DBA 5 (Ev. 2) Utiliza la derivada para estudiar la covariación entre dos magnitudes y relaciona características de la derivada con características de la función.:@0.105897:0.971366:0.919038:0.971366:0.919038:0.959414:0.105897:0.959414:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
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