Differentiation 1 - Basic Polynomial Expressions (with second derivatives)

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Katie Lester 9 years, 7 months ago

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Katie Lester 9 years, 7 months ago

Created this as a copy of Differentiation 1 - Basic Polynomial Expressions.

Name	Status	Author	Last Modified
Differentiation 1 - Basic Polynomial Expressions	Ready to use	Katie Lester	01/06/2016 09:47
Differentiation 2 - Basic Polynomial Expressions	Ready to use	Katie Lester	01/06/2016 09:47
Differentiation 3 - Basic Polynomial Expressions	Ready to use	Katie Lester	01/06/2016 09:47
Differentiation 4 - Trigonometric Functions	Ready to use	Katie Lester	01/06/2016 09:47
Differentiation 5 - Trigonometric Functions	Ready to use	Katie Lester	23/03/2021 15:11
Differentiation 1 - Basic Polynomial Expressions (with second derivatives)	Ready to use	Katie Lester	01/06/2016 09:47
Jinhua's copy of Differentiation 5 - Trigonometric Functions	Ready to use	Jinhua Mathias	27/08/2024 16:37
Jinhua's copy of Differentiation 3 - Basic Polynomial Expressions	Ready to use	Jinhua Mathias	27/08/2024 16:37
Jinhua's copy of Differentiation 2 - Basic Polynomial Expressions	Ready to use	Jinhua Mathias	27/08/2024 16:37
Jinhua's copy of Differentiation 1 - Basic Polynomial Expressions (with second derivatives)	Ready to use	Jinhua Mathias	27/08/2024 16:37
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CF Maths Portfolio - Basic Polynomial Expressions 2	Has some problems	Jinhua Mathias	28/08/2024 12:15
CF Maths Portfolio - Differentiation 1 - Basic Polynomial Expressions (with second derivatives)	Ready to use	Jinhua Mathias	27/08/2024 16:37
CF Maths In class test two mock paper question 1	Ready to use	Jinhua Mathias	28/08/2024 12:15
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Differentiation 1 - Basic Polynomial Expressions	Ready to use	Jinhua Mathias	28/08/2024 12:15
Vicky's copy of Differentiation 1 - Basic Polynomial Expressions	draft	Vicky Hall	01/07/2016 20:46
Basic differentiation	draft	Vicky Hall	25/07/2016 15:52
Jinhua's copy of Differentiation 4 - Trigonometric Functions	draft	Jinhua Mathias	28/08/2024 12:15
Jinhua's copy of Differentiation 5 - Trigonometric Functions	draft	Jinhua Mathias	28/08/2024 12:15
Jinhua's copy of Differentiation 1 - Basic Polynomial Expressions	draft	Jinhua Mathias	28/08/2024 12:15
Jinhua's copy of Differentiation 2 - Basic Polynomial Expressions	draft	Jinhua Mathias	28/08/2024 12:15
Jinhua's copy of Differentiation 1 - Basic Polynomial Expressions (with second derivatives)	draft	Jinhua Mathias	28/08/2024 12:15
Jinhua's copy of Differentiation 2 - Basic Polynomial Expressions	draft	Jinhua Mathias	28/08/2024 12:15
CF Maths Portfolio - Differentiation 2 - Basic Polynomial Expressions (with fractional coefficients)	Ready to use	Jinhua Mathias	27/08/2024 16:37
TRES SEIS Derivadas R potencia y suma/resta	draft	Marlon Arcila	08/09/2021 00:32
CUATRO CUATRO Derivada FT	draft	Marlon Arcila	08/09/2021 00:36
CUATRO TRES Derivada FT	draft	Marlon Arcila	08/09/2021 00:34
TRES DOS Derivadas R potencia y suma/resta	draft	Marlon Arcila	08/09/2021 00:27
TRES TRES Derivadas R potencia y suma/resta	draft	Marlon Arcila	08/09/2021 00:28
TRES CUATRO Derivadas R potencia y suma/resta	draft	Marlon Arcila	08/09/2021 00:29
TRES CINCO Derivadas R potencia y suma/resta	draft	Marlon Arcila	30/11/2021 00:55
CUATRO UNO Derivada FT	draft	Marlon Arcila	08/09/2021 00:33
CUATRO DOS Derivada FT	draft	Marlon Arcila	08/09/2021 00:35
Differentiation of Basic Polynomial Expressions (with second derivatives)	draft	Nigel Atkins	02/03/2017 10:49
cormac's copy of Jinhua's copy of Differentiation 1 - Basic Polynomial Expressions (with second derivatives)	draft	cormac breen	17/04/2020 19:41
cormac's copy of cormac's copy of Jinhua's copy of Differentiation 1 - Basic Polynomial Expressions (with second derivatives)	draft	cormac breen	06/03/2017 14:11
Pascal's copy of Differentiation of Basic Polynomial Expressions (with second derivatives)	draft	Pascal Philipp	07/08/2017 19:25
Ida's copy of TRES CINCO Derivadas R potencia y suma/resta	draft	Ida Landgärds	16/04/2018 12:23
Harry's copy of Differentiation of Basic Polynomial Expressions (with second derivatives)	draft	Harry Flynn	08/05/2018 12:22
Harry's copy of CF Maths Portfolio - Differentiation 2 - Basic Polynomial Expressions (with fractional coefficients)	draft	Harry Flynn	08/05/2018 16:53
Alison's copy of Vicky's copy of Differentiation 1 - Basic Polynomial Expression	draft	Alison Loddick	16/01/2019 15:40
Differentiation 1 - Basic Polynomial Expressions	draft	Xiaodan Leng	11/07/2019 06:54
Differentiation 1 - Basic Polynomial Expressions (with second derivatives)	draft	Xiaodan Leng	11/07/2019 06:55
Differentiation 4 - Trigonometric Functions	draft	Xiaodan Leng	11/07/2019 07:00
Differentiation 5 - Trigonometric Functions	draft	Xiaodan Leng	11/07/2019 07:01
Differentiation - Trigonometric Functions	draft	Kevin Bohan	27/01/2020 14:48
Musa's copy of 3 Differentiation - Trigonometric Functions	draft	Musa Mammadov	27/06/2023 01:34
Differentiation - Trigonometric Functions	Ready to use	Wan Mekwi	26/10/2020 11:35
Chain Rule 3 (H)	Ready to use	Chris Knapp	06/03/2025 11:19
Chain Rule 5 (M)	Ready to use	Chris Knapp	06/03/2025 11:20
Chain Rule 4 (M)	Ready to use	Chris Knapp	06/03/2025 11:20

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Question statement

Differentiate the following polynomials.

Note: some questions may not include all the possible terms.

Give any introductory information the student needs.

			Name	Type	Generated Value

ac	list	[ -1, -1, -3, -1 ]
bc	list	[ -6, 4, -5, 1 ]
cc	list	[ 6, -2, -7, -6 ]
dc	list	[ -7, -3, -13, 1 ]
ec	list	[ -28, 11, 22, 10 ]
fc	list	[ 44, 9, -14, 28 ]
ap	integer	5
bp	integer	4
cp	integer	3
dp	integer	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`

[ -1, -1, -3, -1 ]

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Gap 0. Number entry
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2. Gap Gap 1. Number entry
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Gap-fill

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$\simplify[basic,zeroterm,zerofactor,unitfactor]{{ac[0]}x^5+{bc[0]}x^4+{cc[0]}x^3+{dc[0]}x^2+{ec[0]}x+{fc[0]}}$

$f'(x)=$ Gap 0. $x^4+$ Gap 1. $x^3+$ Gap 2. $x^2+$ Gap 3. $x+$ Gap 4.

$f''(x)=$ Gap 5. $x^3+$ Gap 6. $x^2+$ Gap 7. $x+$ Gap 8.

Advice

If $y=ax^n$ ,

$\frac{dy}{dx}=anx^{n-1}$ for all rational $n$ .

We'll take one of the terms from Part a as an example:

$\var{cc[0]}x^\var{cp}$

All we have to do to terms where $x$ is to a power of anything is times the coefficient of $x$ by the original power, and then take one away from the original power.

If you are not familiar with this kind of work, these instructions may sound confusing, but it is much easier once you have seen it in practice.

We take

$\var{cc[0]}x^\var{cp}$

and times $\var{cc[0]}$ by $\var{cp}$ , to get

$(\var{cc[0]}*\var{cp})x^\var{cp}=\simplify{{cc[0]}*{cp}x^{cp}}$ .

We then subtract one from the original power, $\var{cp}$ .

This gives us the final answer of

$\simplify{{cc[0]}*{cp}x^{cp-1}}$ .

Remember, don't be confused if there is no coefficient. The fact the term is there means the coefficient must be $1$ , but we don't tend to write it out as, for example $1x$ , we just say $x$ .

Give a worked solution to the whole question.

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Differentiation 1 - Basic Polynomial Expressions (with second derivatives)

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Katie Lester 9 years, 7 months ago

Katie Lester 9 years, 7 months ago

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Generated value: `list`

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Gap-fill

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Differentiation 1 - Basic Polynomial Expressions (with second derivatives)

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Katie Lester 9 years, 7 months ago

Katie Lester 9 years, 7 months ago

Error in variable testing condition

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Generated value: list

Parts

Gap-fill

Generated value: `list`