DIfferentiation: product rule

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Christian Lawson-Perfect

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Christian Lawson-Perfect 1 year, 9 months ago

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Sam jemison 1 year, 9 months ago

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Newcastle University Mathematics and Statistics 9 years, 2 months ago

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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

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Question statement

Differentiate the following function $f(x)$ using the product rule.

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	3
s1	integer	-1
b	integer	-5
m	integer	4
n	integer	5

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`

→ Used by:

Advice
"Unnamed part" - prompt
"Unnamed part" → "Unnamed gap" - Correct answer

Parts

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1. Gap Mathematical expression
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1. Step Information only

Gap-fill

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

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

You are given that

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

for a polynomial $g(x)$ . You have to find $g(x)$ .

$g(x)=\;$ Unnamed gap

Click on Show steps to get more information, you will not lose any marks by doing so.

Advice

The product rule says that if $u$ and $v$ are functions of $x$ then

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

For this example:

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

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

Hence on substituting into the product rule above we get:

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

The last step was to take out the common term $\simplify[dPoly]{({a} + {b} * x) ^ {m -1} * e ^ ({n} * x)}$ .

Hence

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

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Christian Lawson-Perfect 1 year, 9 months ago

Sam jemison 1 year, 9 months ago

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

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Generated value: `integer`

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Gap-fill

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DIfferentiation: product rule

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 1 year, 9 months ago

Sam jemison 1 year, 9 months ago

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`