Derivación funciones compuestas
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Cuaderno de trabajo derivadas experiencia 1
This document discusses techniques for finding derivatives of basic functions. It covers finding the derivative of constant functions, which is always 0. It also discusses the derivatives of identity functions (f(x)=x), which is 1, power functions (f(x)=xn), which is nxn-1, square root functions (f(x)=√x), which is 1/2√x, and exponential functions (f(x)=ex), which is ex. Examples are provided for each case along with exercises for students to practice finding derivatives of various functions using the appropriate technique.
Cuaderno de trabajo en derivadas experiencia 2
En presente Cuaderno de trabajo brinda las técnicas de derivación apropiadas en las operaciones con funciones reales.
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En el siguiente Cuaderno de Trabajo se muestran las técnicas de derivación apropiadas para las funciones transcendentes
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S1 0 derivadas
This document defines the derivative and the four step rule for calculating derivatives. It explains that the derivative represents the slope of the tangent line to a function's graph at a given point. The formal definition of the derivative is presented as the limit of the difference quotient. The four step rule outlines the process for calculating the derivative of a function f(x) by adding an increment to x and y, isolating the change in y, dividing by the change in x, and taking the limit as the change in x approaches zero.
Presentation1
The document defines key concepts relating to functions and relations:
- A relation is a set of ordered pairs where the domain is the set of all x-values and the range is the set of all y-values.
- A function is a special type of relation where each x-value is assigned to exactly one y-value.
- Function notation uses f(x) to represent the output of a function f when the input is x.
- The domain of a function is the set of all valid input values that do not result in undefined outputs like division by zero or square roots of negative numbers.
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Cuaderno de trabajo derivadas experiencia 1
This document discusses techniques for finding derivatives of basic functions. It covers finding the derivative of constant functions, which is always 0. It also discusses the derivatives of identity functions (f(x)=x), which is 1, power functions (f(x)=xn), which is nxn-1, square root functions (f(x)=√x), which is 1/2√x, and exponential functions (f(x)=ex), which is ex. Examples are provided for each case along with exercises for students to practice finding derivatives of various functions using the appropriate technique.
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This document defines the derivative and the four step rule for calculating derivatives. It explains that the derivative represents the slope of the tangent line to a function's graph at a given point. The formal definition of the derivative is presented as the limit of the difference quotient. The four step rule outlines the process for calculating the derivative of a function f(x) by adding an increment to x and y, isolating the change in y, dividing by the change in x, and taking the limit as the change in x approaches zero.
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Derivación
1) La derivada de una función representa la tasa de cambio de dicha función y se define como el límite de la pendiente de la recta que une dos puntos cercanos de la gráfica de la función.
2) El documento presenta reglas para calcular derivadas de funciones elementales, operaciones con derivadas y derivadas de funciones compuestas.
3) También introduce conceptos como puntos críticos, máximos y mínimos locales y globales, funciones crecientes y decrecientes, y puntos de inflexión.
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Este documento presenta conceptos básicos sobre la derivada de funciones de una variable, incluyendo su definición, sentido físico y geométrico, reglas para calcular derivadas de funciones elementales y operaciones con funciones, derivadas de funciones compuestas, el teorema del valor medio, la regla de L'Hôpital, y cómo encontrar valores máximos, mínimos, puntos de inflexión, y determinar si una función es creciente o decreciente.
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Derivación funciones compuestas
- 1. DERIVADAS DE FUNCIONES COMPUESTAS Prof: Ing Jocabed Pulido (Esp.) Santa Ana de Coro, septiembre de 2021
- 2. FUNCIONES COMPUESTAS Es una función formada por la composición o aplicación sucesiva de otras funciones. Ejemplo 𝑦 = 𝑥 + 2 3 Ejemplo 𝑦 =Ln 𝑥 + 5 Ejemplo 𝑦 = 𝑒𝑥+1 Funciones Funciones Funciones Función Lineal x+2 Función Potencia Cúbica Función Exponencial Función Lineal x+1 Función logarítmica Función Lineal x+5
- 3. DERIVACIÓN DE FUNCIONES COMPUESTAS Regla de la cadena : Según este método la derivada una función compuesta de la forma 𝑦 = 𝑓 𝑔 𝑥 es igual al siguiente producto 𝑦´ = 𝑓´ 𝑔 𝑥 . 𝑔´ 𝑥 La regla de cadena implica la aplicación de dos pasos importantes a la hora de derivar Paso 1: Derivar la función principal y dejar indica la derivada de la función secundaria. Paso 2: Derivar la función secundaria y presentar el resultado general La que aparece de primera es la función principal f La que aparece de segunda es la función secundaria g
- 4. Ejemplos: Encuentra la derivada de la siguiente función 𝑦 = 𝑥2 − 3𝑥 + 5 3 Paso 1: Derivar la función principal potencia 3 y se deja indicada la derivada de la función secundaria. 𝑦´ = 3 𝑥2 − 3𝑥 + 5 2 . 𝑥2 − 3𝑥 + 5 ´ Paso 2: Derivar la función secundaria y presentar el resultado general 𝑦´ = 3 𝑥2 − 3𝑥 + 5 2 . 2𝑥 − 3
- 5. Ejemplos: Encuentra la derivada de la siguiente función Paso 1: Derivar la función principal y se deja indicada la derivada de la función secundaria. Paso 2: Derivar la función secundaria y presentar el resultado general 𝑦 = 𝑥2 + 3𝑥 𝑦´ = 1 2 𝑥2 + 3𝑥 . 𝑥2 + 3𝑥 ´ 𝑦´ = 1 2 𝑥2 + 3𝑥 . 2𝑥 + 3 𝑦´ = 2𝑥 + 3 2 𝑥2 + 3𝑥
- 6. Ejemplos: Encuentra la derivada de la siguiente función Paso 1: Derivar la función principal exponencial y se deja indicada la derivada de la función secundaria. 𝑦´ = 𝑒𝑡𝑎𝑛 𝑥 . 𝑡𝑎𝑛 𝑥 ´ Paso 2: Derivar la función secundaria y presentar el resultado general 𝑦´ = 𝑒𝑡𝑎𝑛 𝑥 . 𝑠𝑒𝑐2 𝑥 𝑡𝑎𝑛 𝑥 ´ = 𝑠𝑒𝑐2 𝑥 𝑦 = 𝑒𝑡𝑎𝑛 𝑥
- 7. FUNCIÓN DERIVADA 𝑦 = 𝑓 𝑥 𝑛 𝑦´ = 𝑛. 𝑓 𝑥 𝑛−1 . 𝑓´ 𝑥 𝑦 = 𝑒𝑓 𝑥 𝑦´ = 𝑒𝑓 𝑥 . 𝑓´ 𝑥 𝑦 = 𝑐𝑜𝑠 𝑓 𝑥 𝑦´ = 𝑠𝑒𝑛 𝑓 𝑥 . 𝑓´ 𝑥 𝑦 = 𝑠𝑒𝑛 𝑓 𝑥 𝑦´ = −𝑐𝑜𝑠 𝑓 𝑥 . 𝑓´ 𝑥 𝑦 = 𝑡𝑎𝑛 𝑓 𝑥 𝑦´ = 𝑠𝑒𝑐2 𝑓 𝑥 . 𝑓´ 𝑥 𝑦 = 𝑠𝑒𝑐 𝑓 𝑥 𝑦´ = 𝑠𝑒𝑐 𝑓 𝑥 . 𝑡𝑎𝑛 𝑓 𝑥 . 𝑓´ 𝑥 𝑦 = 𝑐𝑜𝑡 𝑓 𝑥 𝑦´ = −𝑐𝑜𝑠𝑒𝑐2 𝑓 𝑥 . 𝑓´ 𝑥 TABLA DE DERIVACIÓN PARA FUNCIONES COMPUESTAS