Differentiation: Quotient rule

Error

There was an error loading the page.

Contributors

Newcastle University Mathematics and Statistics

History

○

Newcastle University Mathematics and Statistics 9 years, 3 months ago

Created this.

Name	Status	Author	Last Modified
Differentiation: Quotient rule	draft	Newcastle University Mathematics and Statistics	20/11/2019 14:50
DOCE UNO Derivadas cociente	draft	Marlon Arcila	08/09/2021 00:42
Luis's copy of Differentiation: Quotient rule	draft	Luis Hernandez	30/11/2018 18:59
diff by quotient rule	draft	Johnny Yi	19/12/2018 01:11

There are 2 other versions that do you not have access to.

Question statement

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

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	7
c	integer	8
b	integer	-1
d	integer	-3
s2	integer	-1
s1	integer	-1
det	integer	-13
c1	integer	8

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.

$\simplify[std]{f(x) = ({a} * x+{b})/({c}x^2+{d})}$
You are given that

$\frac{df}{dx}=\simplify[std]{g(x)/({c}x^2+{d})^2}$
for a polynomial

$g(x)$ . You are asked to find

$g(x)$

$g(x)=\;$ Unnamed gap

Input all numbers as fractions or integers and not as decimals.

Click on Show steps for more information. You will not lose any marks by doing so.

Advice

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

$\simplify[std]{Diff(u/v,x,1) = (v * Diff(u,x,1) - u * Diff(v,x,1))/v^2}$

For this example:

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

$\simplify[std]{v = ({c} * x^2+{d})} \Rightarrow \simplify[std]{Diff(v,x,1) = {2*c}x}$

Hence on substituting into the quotient rule above we get:

$\begin{eqnarray*} \frac{df}{dx}&=&\simplify[std]{({a}({c}x^2+{d})-{2*c}x({a}x+{b}))/({c}x^2+{d})^2}\\ &=&\simplify[std]{({a*c}x^2+{a*d}-{2*c*a}x^2-{2*c*b}x)/({c}x^2+{d})^2}\\ &=&\simplify[std]{({-c*a}x^2+{-2*b*c}x+{a*d})/({c}x^2+{d})^2} \end{eqnarray*}$
Hence

$g(x)=\simplify[std]{{-c*a}x^2+{-2*b*c}x+{a*d}}$

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

Newcastle University Mathematics and Statistics 9 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Loading...

Error

Differentiation: Quotient rule

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Newcastle University Mathematics and Statistics 9 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`