CINCO SEIS Derivada producto

Error

There was an error loading the page.

Contributors

Marlon Arcila

History

○

david arcila was given access to the CINCO SEIS Derivada producto 3 years, 6 months ago

○

Marlon Arcila 8 years, 4 months ago

Created this as a copy of DIfferentiation: product rule.

Name	Status	Author	Last Modified
DIfferentiation: product rule	Ready to use	Newcastle University Mathematics and Statistics	20/06/2023 11:26
CINCO SEIS Derivada producto	draft	Marlon Arcila	08/09/2021 00:40
Differentiation: product and chain rule, (a+bx)^m e^(nx), factorise answer	Ready to use	Lovkush Agarwal	18/06/2018 12:28
Helge's copy of DIfferentiation: product rule	draft	Helge Münnich	28/02/2018 11:26
Helge's copy of DIfferentiation: product rule	Ready to use	Helge Münnich	01/03/2018 01:14
Evan's copy of Differentiation: product and chain rule	draft	Evan Berrett	01/03/2018 15:14
Nick's copy of Differentiation: product and chain rule, (a+bx)^m e^(nx), factorise answer	draft	Nick Walker	22/06/2018 00:44
Vicki's copy of Nick's copy of Differentiation: product and chain rule, (a+bx)^m e^(nx), factorise answer	draft	Vicki Fracarossi	28/06/2018 01:21
Praneetha's copy of Nick's copy of Differentiation: product and chain rule, (a+bx)^m e^(nx), factorise answer	draft	Praneetha Singh	28/06/2018 05:47
Differentiation: product and chain rule, (a+bx)^m e^(nx), factorise answer [L8 Randomised]	Needs to be tested	Matthew James Sykes	25/07/2018 10:54
Differentiation: product and chain rule, (a+bx)^m e^(nx), factorise answer	draft	Xiaodan Leng	11/07/2019 00:11

There are 8 other versions that do you not have access to.

Question statement

Calcular la derivada empleando la regla del Producto.

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	3
s1	integer	-1
b	integer	-4
m	integer	8
n	integer	6

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(1..4)

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `integer`

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap Mathematical expression
  Add
1. Step Mathematical expression

Gap-fill

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

La derivada de la función $\simplify[dPoly]{f(x) = ({a} + {b} * x) ^ {m} * e ^ ({n} * x)}$ es:

$\simplify[dPoly]{Diff(f,x,1) = ({a} + {b} * x) ^ {m -1} * e ^ ({n} * x) * g(x)}$

Determine el polinomio $g(x)$ faltante en la expresión.

$g(x)=\;$ Unnamed gap

Ejemplo de respuesta: escriba 7-8x para ingresar una respuesta como

$7-8x$

Advice

Si $u$ y $v$ son funciones derivables de $x$ , entonces la derivada del producto es:

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

En el ejercicio se tiene que:

$\simplify[dPoly]{u = ({a} + {b} * x) ^ {m}}\Rightarrow \simplify[dPoly]{Diff(u,x,1) = {m * b} * ({a} + {b} * x) ^ {m -1}}$

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

Reemplazando en la fórmula se obtiene:

$\simplify[dPoly]{Diff(f,x,1) = {m * b} * ({a} + {b} * x) ^ {m -1} * e ^ ({n} * x) + {n} * ({a} + {b} * x) ^ {m} * e ^ ({n} * x) = ({a} + {b} * x) ^ {m -1} * ({m * b + n * a} + {n * b} * x) * e ^ ({n} * x)}$

En el último paso se ha factorizado la expresión, tomando factor común: $\simplify[dPoly]{({a} + {b} * x) ^ {m -1} * e ^ ({n} * x)}$ .

De lo anterior se puede concluir que

$\simplify[dPoly]{g(x) = {m * b + n * a} + {n * b} * x}$ .

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet

This question is used in the following exams:

Loading...

Error

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

david arcila was given access to the CINCO SEIS Derivada producto 3 years, 6 months ago

Marlon Arcila 8 years, 4 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Loading...

Error

CINCO SEIS Derivada producto

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

david arcila was given access to the CINCO SEIS Derivada producto 3 years, 6 months ago

Marlon Arcila 8 years, 4 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`