Differentiation 5 Mix questions of the basics in differentiation

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Laura Chiappara

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Laura Chiappara 3 years, 8 months ago

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Julie Crowley 3 years, 8 months ago

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TEAME CIT 9 years ago

Created this as a copy of Differentiation 4 Rule for exponential and natural log.

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 from questions 1 to 4:

For each of the following find $\frac{dy}{dx}$ :

Give any introductory information the student needs.

			Name	Type	Generated Value

num1	list	[ 5, 3, 4, 7, 6 ]
ans11	number	15
ans12	number	2
ans13	number	4
ans14	number	7
ans15	number	6
num2	list	[ 2, 6, 3, 8 ]
num3	list	[ 5, 4, 8, 3 ]
ans31	number	4
ans32	number	3
num4	list	[ 12, 10, 3, 5, 11, 8, 7 ]
ans41	number	120
ans42	number	9
ans43	number	15
ans44	number	-6
ans45	number	3.5
num5	list	[ 4, 5, 7, 3, 10, 8 ]
ans51	number	20
ans52	number	4
ans53	number	3.3333333333
ans54	number	-11
num6	list	[ 11, 6, 12, 9, 5, 7, 4, 3 ]
ans61	number	66
ans62	number	108
ans63	number	35
vs	string	e
num7	list	[ 5, 2 ]
ans7	number	-10

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.

Can an exam override the value of this variable?

Generated value: `list`

[ 5, 3, 4, 7, 6 ]

→ Used by:

ans11
ans12
ans13
ans14
ans15

Advice
"Part a)" - prompt

Parts

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

Gap-fill

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

$y = \var{num1[0]}x^\var{num1[1]} + \var{num1[2]}x + x^\var{num1[3]} + \var{num1[4]}$

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

Advice

$y = \var{num1[0]}x^\var{num1[1]} + \var{num1[2]}x + x^\var{num1[3]} + \var{num1[4]}$

$\frac{dy}{dx} = (\var{num1[1]} \times \var{num1[0]})x^{\var{num1[1]}-1} + \var{num1[2]} + (1 \times \var{num1[3]})x^{\var{num1[3]}-1}$

$\var{ans11}x^(\var{ans12}) + \var{ans13}+ \var{ans14}x^\var{ans15}$

ii)

$y = \var{num2[0]}e^x + \var{num2[1]}x + \ln\var{num2[2]}x + \var{num2[3]}\cos x$

$\frac{dy}{dx} = \var{num2[0]}e^x + \var{num2[1]} + \frac{1}{x} - \var{num2[3]}\sin x$

iii)

$y = x^\var{num3[0]} + x^\var{num3[1]} + \var{num3[2]}x + \var{num3[3]}$

$\frac{dy}{dx} = (1 \times \var{num3[0]})x^{\var{num3[0]}-1} + (1 \times \var{num3[1]})x^{\var{num3[1]}-1} + \var{num3[2]}$

$\var{num3[0]}x^\var{ans31} + \var{num3[1]}x^\var{ans32}+ \var{num3[2]}$

iv)

$y = \var{num4[0]}x^\var{num4[1]} + \frac{\var{num4[2]}}{x^\var{num4[3]}} + \var{num4[4]} - \var{num4[5]}x + \var{num4[6]} \sqrt x$

$\frac{dy}{dx} = (\var{num4[1]} \times \var{num4[0]})x^{\var{num4[1]}-1} + \var{num4[2]}x^{-\var{num4[3]}} - \var{num4[5]} + \var{num4[6]}x^{\frac{1}{2}}$

$(\var{num4[1]} \times \var{num4[0]})x^{\var{num4[1]}-1} + (-\var{num4[3]} \times \var{num4[2]})x^{-\var{num4[3]}-1} - \var{num4[5]} + (\frac{1}{2} \times \var{num4[6]})x^{\frac{1}{2}-1}$

$\var{ans41}x^\var{ans42} - \var{ans43}x^\var{ans44} - \var{num4[5]} + \var{ans45}x^{-\frac{1}{2}}$

$y = \var{num5[0]}x^\var{num5[1]} + \var{num5[2]}x - \frac{1}{\var{num5[3]}x^\var{num5[4]}} + \frac{1}{\sqrt x} - \var{num5[5]}$

$\frac{dy}{dx} = (\var{num5[1]} \times \var{num5[0]})x^{\var{num5[1]}-1} + \var{num5[2]} - \frac{1}{\var{num5[3]}}x^{-\var{num5[4]}} + x^{-\frac{1}{2}}$

$\var{ans51}x^\var{ans52} + \var{num5[2]} + \var{ans53}x^\var{ans54} - \frac{1}{2}x^{-\frac{3}{2}}$

vi)

$y = \var{num6[0]}\sin \var{num6[1]}x + \var{num6[2]}\cos \var{num6[3]}x +\var{num6[4]}e^{\var{num6[5]}x} + \var{num6[6]}\ln\var{num6[7]}x$

$\frac{dy}{dx} = (\var{num6[0]} \times \var{num6[1]})\cos \var{num6[1]}x - (\var{num6[2]} \times \var{num6[3]})\sin \var{num6[3]}x + (\var{num6[4]} \times \var{num6[5]})e^{\var{num6[5]}x} + \var{num6[6]} \times \frac{1}{x}$

$\var{ans61}\cos \var{num6[1]}x - \var{ans62}\sin \var{num6[3]}x + \var{ans63}e^{\var{num6[5]}x} + \frac{\var{num6[6]}}{x}$

vii)

$y = \frac{\var{num7[0]}}{e^{\var{num7[1]}x}} + \var{vs}$

$\frac{dy}{dx} = \var{num7[0]}e^{-\var{num7[1]}x} + \var{vs}$

$(\var{num7[0]} \times -\var{num7[1]})e^{-\var{num7[1]}x} + 0$

$\var{ans7}e^(-\var{num7[1]}x)$

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Differentiation 5 Mix questions of the basics in differentiation

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Laura Chiappara 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 5 Mix questions of the basics in differentiation

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Laura Chiappara 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`