Chain Rule 3 (H)

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Chris Knapp

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Chris Knapp 2 months, 1 week ago

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Chris Knapp 2 months, 1 week ago

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Chris Knapp 1 year, 6 months ago

Created this as a copy of Differentiation - Trigonometric + exp inc chain (4parts).

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
Jinhua's copy of Differentiation 4 - Trigonometric Functions	Ready to use	Jinhua Mathias	27/08/2024 16:37
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
CF Maths In class test two mock paper question 5 (ii)	Ready to use	Jinhua Mathias	28/08/2024 12:15
CF Maths Portfolio 6 - Differentiation of Trigonometric Functions	Ready to use	Jinhua Mathias	28/08/2024 12:15
Bill's copy of CF Maths Portfolio 6 - Differentitation of Trigonometric Functions	Ready to use	Bill Foster	14/09/2016 13:31
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

There are 117 other versions that do you not have access to.

Question statement

Differentiate the following functions.

Do not write out $dy/dx$ ; only input the differentiated right hand side of each equation.

Give any introductory information the student needs.

			Name	Type	Generated Value

			c	list	[ 3, 5, 7, 8, 2 ]
			p	list	[ 3, 4 ]

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xxxxxxxxxx
 
shuffle(2..8)[0..5]

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coefficients

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Generated value: `list`

[ 3, 5, 7, 8, 2 ]

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Parts

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

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

$y=\sin(\var{c[0]}x)$

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

Advice

If you don't know how to differentiate trigonometric functions, please see 'Differentiation 4 - Trigonometric Functions'.

These questions use the chain rule.

The earlier questions are easy to do by inspection, e.g using Part a:

$y=sin(\var{c[0]}x)$ .

We differentiate the term(s) inside the function, here the term is $\var{c[0]}x$ .

Then we derive $sin$ of any function, giving us $cos$ .

Putting our results together, we get

$\var{c[0]}cos(\var{c[0]}x)$ .

We will now go through an entire worked example of the formal method of the chain rule using Part e.

The expression we will be differentiating here is

$y=tan^\var{p[0]}(x)$ .

As a reminder, the chain rule is defined as

$\frac{dy}{dx}=\frac{dy}{du}\times\frac{du}{dx}$ .

Now we let $u=tanx$ , so then $y=u^\var{p[0]}$

This becomes an easy differentiation using $\frac{dy}{du}\times\frac{du}{dx}$ :

Differentiate $y$ with respect to $u$ , giving $\simplify{{p[0]}u^{{p[0]}-1}}$ .

Then differentiate $u$ with respect to $x$ , giving $sec^2x$ .

Multiply these results together, and substitue $tan$ back in for $u$ .

Your final result is therefore

$\simplify{{p[0]}(tan^{{p[0]}-1}(x))*sec^2(x)}$ .

Give a worked solution to the whole question.

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This question is used in the following exams:

Practice Test by Chris Knapp in Chris's workspace.
Practice Test by Chris Knapp in Chris's workspace.
Practice by Chris Knapp in Chris's workspace.
ENG1501 - Mock Test - Unlimited Time (full syllabus) by Zepeng Liu in Zepeng's workspace.

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Chris Knapp 2 months, 1 week ago

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Chris Knapp 1 year, 6 months ago

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Chain Rule 3 (H)

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Taxonomy: mathcentre

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Chris Knapp 2 months, 1 week ago

Chris Knapp 2 months, 1 week ago

Chris Knapp 1 year, 6 months ago

Error in variable testing condition

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Generated value: list

Parts

Gap-fill

Generated value: `list`