Product rule

Error

There was an error loading the page.

Contributors

Bill Foster

History

○

Bill Foster 55 years, 2 months ago

Created this.

There is only one version of this question that you have access to.

There is one other version that you do not have access to.

Question statement

Differentiate the following function $f(x)$ using the product rule. The answer will be of the form

$\simplify[std]{x^{m-1}({a}x+{b})^{n-1}g(x)}$ for a polynomial

$g(x)$ . You have to find

$g(x)$

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	9
s1	integer	1
b	integer	8
m	integer	7
n	integer	7

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`

This variable doesn't seem to be used anywhere.

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.

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

$g(x)=\;$ 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:

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

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

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 used in the following exams:

Loading...

Error

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Bill Foster 55 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Loading...

Error

Product rule

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Bill Foster 55 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`