CINCO CUATRO Derivada producto

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Marlon Arcila

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david arcila was given access to the CINCO CUATRO Derivada producto 3 years, 7 months ago

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Marlon Arcila 8 years, 5 months ago

Created this as a copy of Differentiation: Product rule.

Name	Status	Author	Last Modified
Differentiation: Product rule	draft	Newcastle University Mathematics and Statistics	20/11/2019 14:50
CINCO CUATRO Derivada producto	draft	Marlon Arcila	08/09/2021 00:39
George's copy of Differentiation: Product rule	draft	George Loughlin	06/07/2017 15:16
Helge's copy of Differentiation: Product rule	draft	Helge Münnich	28/02/2018 11:41
Harry's copy of George's copy of Differentiation: Product rule	draft	Harry Flynn	08/05/2018 12:02
Harry's copy of Differentiation: Product rule	draft	Harry Flynn	08/05/2018 12:46
Luis's copy of Differentiation: Product rule	draft	Luis Hernandez	30/11/2018 19:05

There are 23 other versions that do you not have access to.

Question statement

Calcular la derivada de la función, empleano la regla del producto

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	9
b	integer	-5
s2	integer	1
s1	integer	-1
m	integer	5
n	integer	3

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(1..9)

JME function reference

Description

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Generated value: `integer`

This variable doesn't seem to be used anywhere.

Parts

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1. Gap Mathematical expression
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Ask the student a question, and give any hints about how they should answer this part.

$\simplify[std]{f(x) = sin({b}x + {a}) * e ^ ({n} * x)}$

$\displaystyle \frac{df}{dx}=\;$ Unnamed gap

Ejemplo de respuesta: digite 2cos(2+2x)e^(-5x)-5sin(2+2x)e^(-5x) en la barra de respuesta, para ingresar una solución de tipo: $2\cos(2+2x)e^{-5x}-5\sin(2+2x)e^{-5x}$

Advice

Si $u$ y $v$ son funciones derivables de $x$ , entonces

$\simplify[std]{Diff(u * v,x,1) = u * Diff(v,x,1) + v * Diff(u,x,1)}$

Para en ejemplo se tiene que:

$\simplify[std]{u = sin({a} + {b} * x)}\Rightarrow \simplify[std]{Diff(u,x,1) = {b} * cos({a} + {b} * x)}$

$\simplify[std]{v = e ^ ({n} * x)} \Rightarrow \simplify[std]{Diff(v,x,1) = {n} * e ^ ({n} * x)}$

Haciendo la sustitución en la fórmula, se obtiene:

$\begin{eqnarray*}\frac{df}{dx} &=& \simplify[std]{{b} * cos({a} + {b} * x) * e ^ ({n} * x) + {n} * sin({a} + {b} * x) * e ^ ({n} * x)}\\ &=&\simplify[std]{({b}cos({a}+{b}x)+{n}sin({a}+{b}x))e^({n}x)} \end{eqnarray*}$

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This question is used in the following exams:

5 C Derivada: regla del producto by david arcila in WWW Derivadas OK EXAMENES.
16 $y'=f'\ast g$ by david arcila in 2021.

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david arcila was given access to the CINCO CUATRO Derivada producto 3 years, 7 months ago

Marlon Arcila 8 years, 5 months ago

Error in variable testing condition

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Generated value: `integer`

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CINCO CUATRO Derivada producto

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

david arcila was given access to the CINCO CUATRO Derivada producto 3 years, 7 months ago

Marlon Arcila 8 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`