Derivadas. 1ºBACH

Sergio Arroyo, May 7, 2019

Table of Contents

  1. Tasa de variación media.
    1. TASA DE VARIACION MEDIA
  2. Derivada de una función en un punto.
    1. Derivative Function: Without Words
    2. Función derivada
    3. Función derivada
  3. Función derivada. Reglas de derivación.
    1. Introducción a las derivadas
    2. Calculadora de derivadas
    3. 20 derivadas para comprobar lo que sabes
    4. Derivadas
  4. Algunas funciones derivadas.
    1. Derivative of Arccosine Function
    2. Derivative of Arcsine Function
    3. Derivative of Arctangent Function
    4. Derivative of Natural Log Function
    5. Derivative of Sine & Cosine Functions (Quick Investigation)
    6. Derivative of Tangent Function (Investigation)
    7. Derivative of Cosine Function (Intuitive Discovery)
    8. Derivative of Sine Function (Intuitive Discovery)
    9. Derivative of a Product
    10. Derivatives of Inverse Functions
  5. Aplicaciones de las derivadas.
    1. Función, derivada, extremos y curvatura
    2. 3-Way Color-Changing Derivative Grapher

1.

Tasa de variación media.

  • 1. TASA DE VARIACION MEDIA

1.1.

TASA DE VARIACION MEDIA

TASA DE VARIACION MEDIA
TASA DE VARIACION MEDIA
– Joaquín Jiménez Ramos

2.

Derivada de una función en un punto.

  • 1. Derivative Function: Without Words
  • 2. Función derivada
  • 3. Función derivada

2.1.

Derivative Function: Without Words

In the applet below, a function [i]f [/i]is shown (black). [br]Its derivative function, f', is shown in gray. [br][br]Feel free to input any function you'd like. [br][br]Slide the slider to see the physical meaning of the derivative of a function (at a certain input value: x-coordinate of white point) within this graphical context. [br][br][i]How can we sketch the graph of the derivative of a function? Explain. [/i]
Quick Demo (BGM: Andy Hunter)
– Tim Brzezinski

2.2.

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2.3.

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3.

Función derivada. Reglas de derivación.

  • 1. Introducción a las derivadas
  • 2. Calculadora de derivadas
  • 3. 20 derivadas para comprobar lo que sabes
  • 4. Derivadas

3.1.

Introducción a las derivadas

– Sergio Arroyo

3.2.

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3.3.

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3.4.

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4.

Algunas funciones derivadas.

  • 1. Derivative of Arccosine Function
  • 2. Derivative of Arcsine Function
  • 3. Derivative of Arctangent Function
  • 4. Derivative of Natural Log Function
  • 5. Derivative of Sine & Cosine Functions (Quick Investigation)
  • 6. Derivative of Tangent Function (Investigation)
  • 7. Derivative of Cosine Function (Intuitive Discovery)
  • 8. Derivative of Sine Function (Intuitive Discovery)
  • 9. Derivative of a Product
  • 10. Derivatives of Inverse Functions

4.1.

Derivative of Arccosine Function

Shown below is a graph of the function [math]f\left(x\right)=cos^{-1}\left(x\right)[/math]. [br][br]Interact with the applet below for a minute by dragging the white point along the arccosine curve. [br][color=#666666][b]The graph of the derivative of this function will be traced out in gray. [/b][/color] [br][br][color=#0000ff]Without looking it up on another tab, [br]use the SAME LOGIC and METHOD OF IMPLICIT DIFFERENTIATION you used in completing[/color] [url=https://www.geogebra.org/m/Bmt2kHQZ]the derivative of the arcsine function worksheet[/url][color=#cc0000] to find the derivative of the arccosine function.[/color] [br][br]After doing so, enter this function into the input box to see how it compares to your [color=#666666][b]gray trace[/b][/color]!
[color=#cc0000][b]After successfully completing this activity, please go to this worksheet & begin: [/b][/color][br][color=#0000ff][b][url=https://www.geogebra.org/m/TCEnNp5h]Derivative of Arctangent Function[/url][/b][/color][br]
– Tim Brzezinski

4.2.

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4.3.

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4.4.

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4.5.

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4.6.

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4.7.

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4.8.

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4.9.

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4.10.

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5.

Aplicaciones de las derivadas.

  • 1. Función, derivada, extremos y curvatura
  • 2. 3-Way Color-Changing Derivative Grapher

5.1.

Función, derivada, extremos y curvatura

Hacer "click" en el cuadro de texto con la expresión de la función, para ir mostrando información con las derivadas y los puntos y asíntotas que aparecen en el gráfico.
– Javier Cayetano Rodríguez

5.2.

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Information