Chain rule - binomial - Numbas at mathcentre.ac.uk

Error

There was an error loading the page.

Contributors

Feedback

From users who are members of Content created by Newcastle University :

Christian Lawson-Perfect

said

Ready to use

4 years, 4 months ago

From users who are not members of Content created by Newcastle University :

porfirio bustos	said	Ready to use	4 years, 3 months ago
francisco Glezortiz	said	Ready to use	4 years, 5 months ago
Simon Vaughan	said	Ready to use	4 years, 7 months ago

History

○

porfirio bustos 4 years, 3 months ago

Gave some feedback: Ready to use

○

Christian Lawson-Perfect 4 years, 4 months ago

Gave some feedback: Ready to use

○

Christian Lawson-Perfect 4 years, 4 months ago

Saved a checkpoint:

I've replaced $dx$ with $\mathrm{d}x$ and turned off "allow unknown function names" so $x(x+1)$ is interpreted as a multiplication.

Restore this checkpoint

○

francisco Glezortiz 4 years, 5 months ago

Gave some feedback: Ready to use

○

francisco Glezortiz 4 years, 5 months ago

Gave some feedback: Doesn't work

○

francisco Glezortiz 4 years, 5 months ago

Gave some feedback: Needs to be tested

○

Simon Vaughan 4 years, 7 months ago

Gave some feedback: Ready to use

○

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Created this.

Name	Status	Author	Last Modified
Chain rule - binomial	Ready to use	Newcastle University Mathematics and Statistics	04/12/2020 23:48
Harry's copy of Chain rule - binomial,	draft	Harry Flynn	08/05/2018 12:40
Luis's copy of Chain rule - binomial,	draft	Luis Hernandez	30/11/2018 19:11
Musa's copy of 3 Chain rule - binomial,	draft	Musa Mammadov	27/06/2023 01:36
Derivative (Function of a Function)	Ready to use	Shaheen Charlwood	27/10/2022 18:51

There are 26 other versions that do you not have access to.

Question statement

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

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	7
s1	integer	1
b	integer	9
m	integer	3
n	integer	9

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.

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

$\displaystyle \frac{\mathrm{d}f}{\mathrm{d}x}=$ Unnamed gap

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

Advice

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

The chain rule says that if $f(x)=g(h(x))$ then

$\simplify[std]{f'(x) = h'(x)g'(h(x))}$

One way to find $f'(x)$ is to let $u=h(x)$ then we have $f(u)=g(u)$ as a function of $u$ .

Then we use the chain rule in the form:

$\frac{\mathrm{d}f}{\mathrm{d}x} = \frac{\mathrm{d}u}{\mathrm{d}x}\frac{\mathrm{d}f(u)}{\mathrm{d}u}$

Once you have worked this out, you replace $u$ by $h(x)$ and your answer is now in terms of $x$ .

For this example, we let $u=\simplify[std]{{a} * x^{m}+{b}}$ and we have $f(u)=\simplify[std]{u^{n}}$ .

This gives

$\begin{align} \frac{\mathrm{d}u}{\mathrm{d}x} &= \simplify[std]{{m*a}x ^ {m -1}} \\[1em] \frac{\mathrm{d}f(u)}{\mathrm{d}u} &= \simplify[std]{{n}u^{n-1}} \end{align}$

Hence on substituting into the chain rule above we get:

$\begin{align} \frac{\mathrm{d}f}{\mathrm{d}x} &= \simplify[std]{{m*a}x ^ {m-1} * ({n}*u^{n-1})} \\ &= \simplify[std]{{m*a*n}x^{m-1}u^{n-1}} \\ &= \simplify[std]{{m*a*n}x^{m-1}({a}*x^{m}+{b})^{n-1}} \end{align}$

on replacing $u$ by $\simplify[std]{{a}x^{m}+{b}}$ .

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:

Differentiation using the chain rule by Newcastle University Mathematics and Statistics in Content created by Newcastle University.
Differentiation using the chain rule by Henrik Skov Midtiby in SDS.
Gareth's copy of Differentiation using the chain rule by Gareth Woods in Gareth's workspace.
Differentiation using the chain rule by Cyprian Omari in Cyprian's workspace.
Cyprian's copy of Differentiation using the chain rule by Cyprian Omari in Cyprian's workspace.
Differentiation using the chain rule by Marlon Arcila in Derivadas.
Differentiation using the chain rule by Marlon Arcila in Derivadas.
Differentiation using the chain rule by Marlon Arcila in Derivadas.
Differentiation using the chain rule by Marlon Arcila in Derivadas.
Differentiation using the chain rule by Marlon Arcila in Derivadas.
Luis's copy of Differentiation using the chain rule by Luis Hernandez in MAT333.
Maria's copy of Differentiation using the chain rule by Maria Aneiros in Maria's workspace.
Ann's copy of Differentiation using the chain rule by Ann Smith in Calculus.
Differentiation using the chain rule by Ann Smith in Calculus.
Differentiation using the chain rule by Jeremie Wenger in Jeremie's workspace.
Differentiation using the chain rule by Ann Smith in FNU Mathematics Fundamentals.
Musa's copy of Differentiation using the chain rule by Musa Mammadov in Musa's workspace.
Newcastle University Differentiation by Nicolas Sawyer in Nicolas's workspace.
Print copy of Differentiation - part 3 by Nicolas Sawyer in Nicolas's workspace.
Simon's copy of Practice for year 1 by Simon Vaughan in PA1710.
Test Exam by Cameline Nafula in Cameline's workspace.
group theory from newcastle by Daniel Chan in Daniel's workspace.
test 1 by Björn Rüffer in Björn's workspace.
Paul's copy of Practice for year 1 by Paul Verheyen in Paul's workspace.
Derivadas- Regla de la cadena by francisco Glezortiz in francisco's workspace.
Practice for year 1 by Simon Vaughan in PA1710.
Theme Test 2 by Michael Guy in Michael's workspace.
Differentiation using the chain rule by Wan Mekwi in Introduction to Calculus.
CEG1716: CBA1 - Practice by Ryan Doran in NCL CEG1716.
Ryan's copy of CEG1716: CBA1 - Practice by Ryan Doran in NCL CEG1716.
Differentiation using the chain rule by Stefania Sitzia in Week 07.
Melissa's copy of Practice for year 1 by Melissa Heath in Melissa's workspace.
Differentiation - chain rule by Jinhua Mathias in Maths 3-2020.
Test - Practice Exam 1 by Tim Wilkinson in Tim's workspace.
Assignment 1 by Kyle Harvey in Kyle's workspace.
chain rule by Jinhua Mathias in Maths 2.
demo exam by john krupej in john's workspace.
diagnostic mode 3 - mastery by Hanne Deprez in Hanne's workspace.
test diagnostic mode 2 by Hanne Deprez in Hanne's workspace.
Maths Techniques - Differentiation - part 3 by Nicolas Sawyer in Nicolas's workspace.
Novry's copy of Practice for year 1 by Novry Erwina in Novry's workspace.
Database Test by Donna Thompson in Donna's workspace.
Differentiation rules by Anita Campbell in Anita's workspace.
homework I by Kuldeep Singh in Kuldeep's workspace.
Chain Rule for Demo by Jinhua Mathias in Jinhua's workspace.
Chain Rule Demo by Jinhua Mathias in Jinhua's workspace.
Kettenregel - Testversion by Benjamin Bertsche in Benjamin's workspace.
chain rule by Mike Phipps in Intro Maths.
Maths Techniques - Differentiation - part 3 short by Nicolas Sawyer in Nicolas's workspace.
Awesome calculus exam by Jamie Antoun in Jamie's workspace.
CEG1716: CBA1 - Assessed by Christian Lawson-Perfect in NCL CEG1716.
Robert's copy of Differentiation using the chain rule by Robert Barham in Robert's workspace.
Quiz2 by Matt Falk in Matt's workspace.
test4 by ahmad mustafa in ahmad's workspace.
claire's copy of Differentiation using the chain rule by claire lines in claire's workspace.
CEG1716 Assessment 1 assessed by James Waldron in NCL CEG1716.
CEG1716 Assessment 1 practice by James Waldron in NCL CEG1716.
The Chain Rules-competition by ahmad mustafa in ahmad's workspace.
CEG1716 Assessment 1 practice 2022/2023 by James Waldron in NCL CEG1716.
All the good stuff by Chris Templet in Chris's workspace.
W09: Differentiation by Alastair Ball in IQT.
W09: Differentiation by Alastair Ball in QTEF1.
CEG1716 Assessment 1 assessed 2022/2023 by James Waldron in NCL CEG1716.
Testing by Nargiz Sultanova in Nargiz's workspace.
Differentiation by Joseph Dessi in NCL CEG1716.
CEG1716 Assessment 1 assessed 2023/24 by Joseph Dessi in NCL CEG1716.
CEG1716 Assessment 1 practice 2023/24 by Joseph Dessi in NCL CEG1716.
W07 23-24 by Jose Camarena Brenes in EMSE.
Mock 1 by ahmad mustafa in EmSAT.
Chain Rule by Luke Middleton in Luke's workspace.
Open day Numbas taster by Christian Lawson-Perfect in Christian's workspace.

Loading...

Error

Chain rule - binomial

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

porfirio bustos 4 years, 3 months ago

Christian Lawson-Perfect 4 years, 4 months ago

Christian Lawson-Perfect 4 years, 4 months ago

francisco Glezortiz 4 years, 5 months ago

francisco Glezortiz 4 years, 5 months ago

francisco Glezortiz 4 years, 5 months ago

Simon Vaughan 4 years, 7 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

Loading...

Error

Chain rule - binomial

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

porfirio bustos 4 years, 3 months ago

Christian Lawson-Perfect 4 years, 4 months ago

Christian Lawson-Perfect 4 years, 4 months ago

francisco Glezortiz 4 years, 5 months ago

francisco Glezortiz 4 years, 5 months ago

francisco Glezortiz 4 years, 5 months ago

Simon Vaughan 4 years, 7 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`