Heather's copy of Differentiation : Product Rule

Error

There was an error loading the page.

Contributors

History

○

Heather Driscoll 6 years, 1 month 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 SIETE Derivada producto	draft	Marlon Arcila	08/09/2021 00:41
Adrian's copy of Differentiation: Product rule	draft	Adrian Jannetta	16/08/2023 14:56
Differentiation: Product rule	draft	Harry Flynn	08/05/2018 11:25
Harry's copy of Adrian's copy of Differentiation: Product rule	draft	Harry Flynn	08/05/2018 11:39
Luis's copy of Differentiation: Product rule	draft	Luis Hernandez	30/11/2018 19:04
Differentiation : Product Rule	draft	Johnny Yi	08/12/2020 02:17
Standard Differentiation	draft	Heather Driscoll	11/02/2019 13:23
Heather's copy of Differentiation : Product Rule	draft	Heather Driscoll	11/02/2019 13:14
Heather's copy of Differentiation : Product Rule	draft	Heather Driscoll	11/02/2019 13:22
Standard Integration	draft	Heather Driscoll	11/02/2019 13:59
Standard Differentiation (Trig)	draft	Heather Driscoll	01/03/2019 12:20
Standard Differentiation (Trig2)	draft	Heather Driscoll	21/09/2022 16:14
JD's copy of Differentiation: Product rule	draft	JD Ichwan	21/05/2019 05:38

There are 24 other versions that do you not have access to.

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	7
s1	integer	1
b	integer	6
m	integer	8
n	integer	3

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(2..9)

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

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

Gap-fill

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

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

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

Clicking on Show steps gives you 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

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

For this example:

$\simplify[std]{u = x ^ {m}}\Rightarrow \simplify[std]{Diff(u,x,1) = {m}x ^ {m -1}}$

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

Hence on substituting into the product rule above we get:

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

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
Information only

This question is not used in any exams.

Loading...

Error

Heather's copy of Differentiation : Product Rule

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Heather Driscoll 6 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Loading...

Error

Heather's copy of Differentiation : Product Rule

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Heather Driscoll 6 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`