Differentiation 4 Rule for exponential and natural log

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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 2 General Rule for fractional and negative indices.

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 rules:

$y = e^ x => \frac{dy}{dx} = e^ x$

$y = e^ {ax} => \frac{dy}{dx} = ae^ {ax}$

$y = \ln (x) => \frac{dy}{dx} = \frac{1}{x}$

$y = \ln (ax) => \frac{dy}{dx} = \frac{1}{x}$

Differentiate each of the following:

Give any introductory information the student needs.

			Name	Type	Generated Value

num	list	[ 6, 7, 5, 8, 4 ]
ans1	number	6
ans2	number	1.5
ans3	number	-35
num2	integer	-5
num1	number	1.5

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
shuffle(2..8)[0..5]

JME function reference

Description

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

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Generated value: `list`

[ 6, 7, 5, 8, 4 ]

→ Used by:

ans1
ans3

This variable doesn't seem to be used anywhere.

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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Part c) Gap-fill
1. Gap Mathematical expression
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Part d) Gap-fill
1. Gap Mathematical expression
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Part e) Gap-fill
1. Gap Mathematical expression
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Part f) Gap-fill
1. Gap Mathematical expression
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Gap-fill

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

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

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

Advice

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

$\frac{dy}{dx} = \var{ans1}e^{\var{num[0]}x}$

ii)

$y = e^{\var{num1}x}$

$\frac{dy}{dx} = \var{ans2}e^{\var{num1}x}$

iii)

$y = \var{num[1]}e^{\var{num2}x}$

$\frac{dy}{dx} = (\var{num[1]} \times \var{num2})e^{\var{num2}x} = \var{ans3}e^{\var{num2}x}$

iv)

$y = \ln \var{num[2]}x$

$\frac{dy}{dx} = \frac{1}{x}$

$y = \ln \var{num[3]}x$

$\frac{dy}{dx} = \frac{1}{x}$

vi)

$y = \ln \var{num[4]}x$

$\frac{dy}{dx} = \frac{1}{x}$

Give a worked solution to the whole question.

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Differentiation 4 Rule for exponential and natural log

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Taxonomy: mathcentre

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Taxonomy: Context

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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`

Parts

Gap-fill

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Differentiation 4 Rule for exponential and natural log

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`