Jinhua's copy of Differentiation 5 - Trigonometric Functions

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Created this as a copy of Differentiation 5 - Trigonometric Functions.

Name	Status	Author	Last Modified
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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
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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
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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
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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
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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
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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 trigonometric functions using the chain rule.

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	[ 8, 5, 2, 6, 4 ]
			p	list	[ 3, 5 ]

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Name

Data type

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xxxxxxxxxx
 
shuffle(2..8)[0..5]

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coefficients

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Generated value: `list`

[ 8, 5, 2, 6, 4 ]

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Parts

Part a) Gap-fill
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Part b) Gap-fill
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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

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

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Jinhua's copy of Differentiation 5 - Trigonometric Functions

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Deactivated user 8 years, 6 months ago

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Jinhua's copy of Differentiation 5 - Trigonometric Functions

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Deactivated user 8 years, 6 months ago

Error in variable testing condition

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Warning

Generated value: list

Parts

Gap-fill

Generated value: `list`