Differentiation 13 - Quotient Rule - Numbas at mathcentre.ac.uk

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Xiaodan Leng 5 years, 9 months ago

Created this as a copy of Differentiation 13 - Quotient Rule.

Name	Status	Author	Last Modified
Differentiation 13 - Quotient Rule	Ready to use	Katie Lester	01/06/2016 09:47
Jinhua's copy of Differentiation 13 - Quotient Rule	Ready to use	Jinhua Mathias	27/08/2024 16:37
Jinhua's copy of Differentiation 13 - Quotient Rule	Ready to use	Jinhua Mathias	27/08/2024 16:37
CF Maths Portfolio - Differentiation 13 - Quotient Rule	Ready to use	Jinhua Mathias	28/08/2024 12:15
Jinhua's copy of CF Maths Portfolio - Differentiation 13 - Quotient Rule	Ready to use	Jinhua Mathias	28/08/2024 12:15
Cf Maths In class test two mock paper question 7 (i)	Ready to use	Jinhua Mathias	28/08/2024 12:15
Andrew's copy of Differentiation 13 - Quotient Rule	Ready to use	Andrew Dunbar	01/06/2016 09:47
Milena's copy of Andrew's copy of Differentiation 13 - Quotient Rule	draft	Milena Venkova	06/03/2018 14:44
Quotient Rule	draft	Milena Venkova	27/02/2018 15:12
Quotient Rule 2	draft	Milena Venkova	08/03/2018 15:49
Milena's copy of Quotient Rule	draft	Milena Venkova	08/03/2018 15:44
Quotient Rule 3	draft	Milena Venkova	13/03/2018 13:53
Differentiation 13 - Quotient Rule	draft	Harry Flynn	08/05/2018 11:37
Differentiation 13 - Quotient Rule	draft	haifa abd	24/05/2018 09:57
Differentiation 13 - Quotient Rule	draft	haifa abd	24/05/2018 09:58
Differentiation 13 - Quotient Rule	draft	haifa abd	24/05/2018 09:58
Differentiation 13 - Quotient Rule	draft	haifa abd	24/05/2018 09:58
Differentiation 13 - Quotient Rule	draft	Xiaodan Leng	11/07/2019 06:57

There are 11 other versions that do you not have access to.

Question statement

Differentiate the following expressions with respect to $x$ using the quotient rule.

Simplify your answers as much as possible.

Give any introductory information the student needs.

			Name	Type	Generated Value

			c	list	List of 12 items
			p	list	[ 6, 2, 2, 7, 6, 7 ]

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Name

Data type

Value

xxxxxxxxxx
 
repeat(random(-9..9 except 0),12)

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Description

Describe what this variable represents, and list any assumptions made about its value.

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Generated value: `list`

[ 2, 6, 1, 5, 2, 5, 1, 5, -4, 4, -8, -4 ]

This variable doesn't seem to be used anywhere.

Advice

These questions use the quotient rule.

The quotient rule is defined as

$\frac{dy}{dx}=\frac{v\frac{du}{dx}+u\frac{dv}{dx}}{v^2}$

when $y=\frac{u}{v}$

Worked example using Part a:

$x$ $\simplify{x+{c[0]}}$

This expression is the result of $x$ divided by ( $\simplify{x+{c[0]}}$ ).

We can therefore say:

$u=x$

and

$v=\simplify{x+{c[0]}}$ ,

Hence meaning that $y=\frac{u}{v}$ .

We already have what $u$ and $v$ equal, so all we have to do is find what $\frac{du}{dx}$ and $\frac{dv}{dx}$ are, and then substitute everything into the rule.

Differentiating with respect to $x$ , we get:

$\frac{du}{dx}=1$

and

$\frac{dv}{dx}=1$ .

As there are no powers or coefficients of $x$ that are $>1$ , this is a very simple version of the quotient rule, but knowing how to work out this equation formally will make more difficult looking problems just as simple.

Substituting in all the results we've found, we get:

$\frac{dy}{dx}=\frac{1(\simplify{x+{c[0]}})+1(x)}{\simplify{(x+{c[0]})^2}}$

We then simplify, collecting all the terms, to get our final answer of:

$\frac{dy}{dx}=\simplify{((2x+{c[0]}))/(x+{c[0]})^2}$

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Differentiation 13 - Quotient Rule

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Xiaodan Leng 5 years, 9 months ago

Error in variable testing condition

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Differentiation 13 - Quotient Rule

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Xiaodan Leng 5 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Mathematical expression

Advanced settings

Checking accuracy

Variable value generators

Pattern restriction

Variables

String restrictions

Generated value: `list`