{} new Polynomial(randRange(0, 3), randRange(2, 4)) POLYNOMIAL.text() POLYNOMIAL.derivative().text() function(x) {return POLYNOMIAL.evalOf(x);} function(x) {return POLYNOMIAL.derivative().evalOf(x);} [-2, -1.5, -1, 0, 1, 1.5, 2] [-2.5, 2.5] min.apply(Math, $.map(POINTS, FNX).concat( $.map(POINTS, DDX))) max.apply(Math, $.map(POINTS, FNX).concat( $.map(POINTS, DDX))) [floorTo(-1, YMIN - (YMAX-YMIN)*0.05 ), ceilTo(-1, YMAX + (YMAX-YMIN)*0.05)] {}

f(x) = FNXTEXT

Arrastra cada uno de los puntos POINTS.length naranjas hacia arriba y abajo para ajustar la pendiente de la recta tangente correspondiente.

La derivada de una función está definida como la pendiente de la recta tangente a una curva en cada punto. Ajusta las pendientes de las rectas para encontrar visualmente la derivada \frac{d}{dx} f(x) en cada punto.

initAutoscaledGraph([XRANGE,YRANGE],OPTIONS),style({stroke:"#6495ED",strokeWidth:3},function(){plot(function(t){return FNX(t)},XRANGE)}),initDerivativeIntuition(FNX,DDX,POINTS)
\frac{d}{dx} f(OPTIONS.xLabelFormat(X)) = \frac{d}{dx} f(X) = 0
function(){var t=[];return $("#answers").find(".answer-label").each(function(){t.push(parseFloat($(this).text()))}),t}()
var t=_(guess).all(function(t){return 0===t});if(t)return"";var n=_(points).map(function(t){return roundTo(2,ddx(t))});return guess.join()===n.join()
_(guess).each(function(t,n){setSlope(n,t)});var correct=_(points).map(function(t){return roundTo(2,ddx(t))});guess.join()===correct.join()&&revealDerivative(0)
$("#answers").find(".answer-label").each(function(t,n){$(n).text(guess.length?guess[t]:0)})

La curva anaranjada muestra la derivada de f(x). Arrastra todos los puntos anaranjados a la curva anaranjada. Observa como las rectas tangentes cambian mientras mueves los puntos anaranjados. Pon atención a la relación entre las rectas tangentes y la curva azul.

revealDerivative()
randFromArray([{text:"sin(x)",ddxtext:"cos(x)",fnx:function(t){return Math.sin(t)},ddx:function(t){return Math.cos(t)},xrange:[-1.25*Math.PI,1.25*Math.PI],yrange:[-1.25,1.25],points:[-1*Math.PI,-3*Math.PI/4,-Math.PI/2,-Math.PI/4,0,Math.PI/4,Math.PI/2,3*Math.PI/4,Math.PI],options:{xLabelFormat:piFraction}},{text:"cos(x)",ddxtext:"-sin(x)",fnx:function(t){return Math.cos(t)},ddx:function(t){return-Math.sin(t)},xrange:[-1.25*Math.PI,1.25*Math.PI],yrange:[-1.25,1.25],points:[-1*Math.PI,-3*Math.PI/4,-Math.PI/2,-Math.PI/4,0,Math.PI/4,Math.PI/2,3*Math.PI/4,Math.PI],options:{xLabelFormat:piFraction}},{text:"e^x",ddxtext:"e^x",fnx:function(t){return Math.exp(t,Math.E)},ddx:function(t){return Math.exp(t,Math.E)},xrange:[-5,5],yrange:[-5,15],points:[-2,-1,0,1,2],options:{}},{text:"ln(x)",ddxtext:"\\frac{1}{x}",fnx:function(t){return Math.log(t)},ddx:function(t){return 1/t},xrange:[.001,5],yrange:[-5,5],points:[.25,.5,1,2,3,4],options:{range:[[-.25,4.75],[-5,5]]}}]) SCENARIO.text SCENARIO.ddxtext SCENARIO.fnx SCENARIO.ddx SCENARIO.xrange SCENARIO.yrange SCENARIO.points SCENARIO.options || {}