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Derivadas: fundamentos y reglas

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Derivadas: fundamentos y reglas

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Conceptos básicos de derivadas

Created by

Luisa Magdiel
Luisa Magdiel
Mexico

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Derivadas: fundamentos y reglas
 

Derivadas: fundamentos y reglasOnline version

Conceptos básicos de derivadas

by Luisa Magdiel
1

¿Qué representa la derivada de una función en un punto?

2

Regla de la suma: la derivada de f(x)=g(x)+h(x) es

3

¿Cuál es la derivada de una constante c?

4

Derivada de x

5

Regla de potencia

6

se usa cuando

7

Usando esta formula, siempre va primero

8

¿Cuál es la derivada de la función f(x)=8x cúbica?

9

Si una función f(x) es derivable en un punto, ¿qué podemos afirmar sobre la continuidad de f(x) en ese punto?

10

Si la segunda derivada de una función, f′(x), es negativa en un intervalo, ¿qué nos indica eso sobre la gráfica de la función f(x) en ese intervalo?

Explicación

La derivada mide la pendiente de la tangente en un punto, es la tasa de cambio instantánea.

La derivada es lineal: la derivada de la suma es la suma de las derivadas.

Las constantes no cambian, su tasa de cambio es cero.

Es 1

La derivabilidad en un punto implica que la función es continua en ese punto. Sin embargo, lo contrario no siempre es cierto

Un valor negativo de la segunda derivada ( f′′(x)<0) en un intervalo indica que la función es cóncava hacia abajo en ese intervalo.

 
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