Differentiation 2 General Rule for fractional and negative indices

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Julie Crowley

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3 years, 8 months ago

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Julie Crowley 3 years, 8 months ago

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Julie Crowley 3 years, 8 months ago

Gave some feedback: Ready to use

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TEAME CIT 9 years ago

Created this as a copy of Differentiation 1 General Rule.

Name	Status	Author	Last Modified
Differentiation 1 General Rule	Ready to use	TEAME CIT	10/07/2021 21:13
Differentiation 2 General Rule for fractional and negative indices	Ready to use	TEAME CIT	10/07/2021 21:13
Differentiation 4 Rule for exponential and natural log	Ready to use	TEAME CIT	10/07/2021 21:13
Differentiation 5 Mix questions of the basics in differentiation	Ready to use	TEAME CIT	19/07/2021 05:36

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Question statement

Remember the rule:

If $y = ax^n$ then $\frac{dy}{dx} = anx^{n-1}$

Differentiate each of the following:

Give any introductory information the student needs.

			Name	Type	Generated Value

p2	list	[ 5, 7 ]
num	list	[ 2, 4 ]
ans11	rational	1/2
ans12	rational	-1/2
ans21	rational	5/7
ans22	rational	-2/7
ans31	number	-6
ans32	integer	-4
p1	integer	2
p3	integer	-3
ans41	number	2
ans42	number	-0.5
ans51	integer	-24
n51	integer	4
n52	integer	6
ans52	integer	-7
n6	integer	7
ans61	rational	7/2
ans62	rational	5/2

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Name

Data type

Value

xxxxxxxxxx
 
shuffle(3..7 except 6)[0..2]

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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`

[ 5, 7 ]

→ Used by:

ans21

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Parts

Part a) Gap-fill
1. Gap Mathematical expression
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Part b) Gap-fill
1. Gap Mathematical expression
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1. Step Information only
Part c) Gap-fill
1. Gap Mathematical expression
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1. Step Information only

Gap-fill

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

$y = \var{num[0]}x^{\var{p3}}$

$\frac{dy}{dx} =$ Unnamed gap

Advice

$y = x^{\frac{1}{\var{p1}}}$

$\frac{dy}{dx} = \var{ans11}x^{(\frac{1}{\var{p1}}-1)} = \var{ans11}x^{\var{ans12}}$

ii)

$y = x^{\frac{\var{p2[0]}}{\var{p2[1]}}}$

$\frac{dy}{dx} = \frac{\var{p2[0]}}{\var{p2[1]}}x^{(\frac{\var{p2[0]}}{\var{p2[1]}}-1)} = \var{ans21}x^{\var{ans22}}$

iii)

$y = \var{num[0]}x^{\var{p3}}$

$\frac{dy}{dx} = \var{ans31}x^{(\var{p3}-1)} = \var{ans31}x^{\var{ans32}}$

iv)

$y = \var{num[1]}\sqrt(x) = \var{num[1]}x^{\frac{1}{2}}$

$\frac{dy}{dx} = \frac{\var{num[1]}}{2}x^{(\frac{1}{2}-1)} = \var{ans41}x^{\var{ans42}}$

$y = \frac{\var{n51}}{x^{\var{n52}}} = \var{n51}x^{-\var{n52}}$

$\frac{dy}{dx} = \var{ans51}x^{(-\var{n52}-1)} = \var{ans51}x^{\var{ans52}}$

vi)

$y = \sqrt(x^\var{n6}) = x^{\frac{\var{n6}}{2}}$

$\frac{dy}{dx} = \frac{\var{n6}}{2}x^{(\frac{\var{n6}}{2}-1)} = \var{ans61}x^{\var{ans62}}$

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Differentiation 2 General Rule for fractional and negative indices

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Julie Crowley 3 years, 8 months ago

Julie Crowley 3 years, 8 months ago

TEAME CIT 9 years ago

Error in variable testing condition

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Generated value: `list`

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Differentiation 2 General Rule for fractional and negative indices

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Julie Crowley 3 years, 8 months ago

Julie Crowley 3 years, 8 months ago

TEAME CIT 9 years ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Gap-fill

Generated value: `list`