Differentiation: Using a Table of Derivatives 5c

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3 years, 8 months ago

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Ben McGovern 2 years, 6 months ago

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Created this as a copy of Differentiation: Using a Table of Derivatives 5a.

Name	Status	Author	Last Modified
Differentiation: Using a Table of Derivatives 2	Ready to use	Ben McGovern	26/09/2022 12:10
Differentiation: Using a Table of Derivatives 3	Ready to use	Ben McGovern	26/09/2022 12:11
Differentiation: Using a Table of Derivatives 4	Ready to use	Ben McGovern	26/09/2022 12:11
Differentiation: Using a Table of Derivatives 5a	Ready to use	Ben McGovern	26/09/2022 12:11
Differentiation: Using a Table of Derivatives 5b	Ready to use	Ben McGovern	26/09/2022 12:12
Differentiation: Using a Table of Derivatives 5c	Ready to use	Ben McGovern	26/09/2022 12:12
Differentiation (Harder powers - negative and fractions) 2	Ready to use	Ben McGovern	04/05/2023 05:42
Differentiation: Stationary Points and their Nature 1	Ready to use	Ben McGovern	26/09/2022 11:56
Differentiation: Stationary Points and their Nature 2	Ready to use	Ben McGovern	26/09/2022 11:56
Integration: Using a Table of Integrals 2	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: Using a Table of Integrals 3a	Ready to use	Ben McGovern	13/02/2023 10:37
Integration: Using a Table of Integrals 3b	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: Using a Table of Integrals 4	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: Using a Table of Integrals 5a	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: Using a Table of Integrals 5b	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: Using a Table of Integrals 5c	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: Using a Table of Integrals 6	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: By Substitution 1a i	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: By Substitution 1b	Ready to use	Ben McGovern	23/02/2023 12:45
Integration: By Substitution 1c	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: By Substitution 2a	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: By Substitution 2b	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: By Substitution 2c	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: By Substitution 3a i	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: By Substitution 3c	Ready to use	Ben McGovern	27/09/2022 09:01
Integration (Negative and Fractional Powers) 2	Has some problems	Ben McGovern	27/09/2022 09:01
Integration (Negative and Fractional Powers) 3	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: Definite Integrals 2	Ready to use	Ben McGovern	26/09/2022 12:18
Integration: By Substitution 1a ii (Negative and Fractional Powers)	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: By Substitution 3a ii (Negative and Fractional Powers)	Ready to use	Ben McGovern	27/09/2022 09:01
Integration: Definite Integrals 3	Ready to use	Ben McGovern	26/09/2022 12:18
Integration: Definite Integrals 4	Ready to use	Ben McGovern	26/09/2022 12:19
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CD3 Integration - Substitution	Ready to use	Andrew Neate	09/04/2024 15:56
CB4 Definite integration	Ready to use	Andrew Neate	09/04/2024 15:45
CB6 Differentiating Trig 1	Ready to use	Andrew Neate	09/04/2024 15:46
CB7 Differentiating Trig 2	Ready to use	Andrew Neate	09/04/2024 15:46
CB8 Differentiating with Trig 3	Ready to use	Andrew Neate	09/04/2024 15:52
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CB3 - Indefinite integration - polynomials	Ready to use	Andrew Neate	09/04/2024 15:45
CB5 - Finding turning points	Ready to use	Andrew Neate	09/04/2024 15:46

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Question statement

Using the Table of Derivatives, calculate the derivative of $y=\simplify[unitFactor]{{a}tan({b}x+{c})}.$

Give any introductory information the student needs.

			Name	Type	Generated Value

			Name	Type	Generated Value

a	integer	10
b	integer	-4
c	integer	9

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Name

Data type

Value

xxxxxxxxxx
 
random(-10..10 except 0)

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Generated value: `integer`

→ Used by:

Statement
Advice
"Unnamed part" → "Gap 0" - Correct answer

Parts

Gap-fill
1. Gap Gap 0 Mathematical expression
  1. Alt Unnamed alternative
  Add

Gap-fill

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

$\frac{dy}{dx}=$ Gap 0

Advice

From the Table of Derivatives we see that a function of the form

$f(x)=a \tan(kx+c)$ has a derivative

$ak \sec^2(kx+c).$

Therefore, the function

$y=\simplify[unitFactor]{{a}*tan({b}x+{c})}$ has a derivative

$\begin{split} \frac{dy}{dx} &=(\var{a}\times \var{b})\sec^2(\simplify[unitFactor]{{b}x+{c}})\\ &= \simplify[unitFactor]{{a*b}}\sec^2(\simplify[unitFactor]{{b}x+{c}}).\end{split}$

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This question is used in the following exams:

Differentiation using a Table of Derivatives by Ben McGovern in MASH Bath: Moodle quizzes and TS.
Test 1 by ahmad mustafa in ahmad's workspace.
All the good stuff by Chris Templet in Chris's workspace.
Remediëring afgeleiden 2 by Hans Denayer in Hans's workspace.

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Differentiation: Using a Table of Derivatives 5c

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Ben McGovern 2 years, 6 months ago

Ben McGovern 3 years, 8 months ago

Ben McGovern 4 years, 9 months ago

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Differentiation: Using a Table of Derivatives 5c

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Ben McGovern 2 years, 6 months ago

Ben McGovern 3 years, 8 months ago

Ben McGovern 4 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`