Differentiation: Product rule

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Newcastle University Mathematics and Statistics

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Newcastle University Mathematics and Statistics 9 years, 2 months ago

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Name	Status	Author	Last Modified
Differentiation: Product rule	draft	Newcastle University Mathematics and Statistics	20/11/2019 14:50
CINCO SIETE Derivada producto	draft	Marlon Arcila	08/09/2021 00:41
Adrian's copy of Differentiation: Product rule	draft	Adrian Jannetta	16/08/2023 14:56
Differentiation: Product rule	draft	Harry Flynn	08/05/2018 11:25
Harry's copy of Adrian's copy of Differentiation: Product rule	draft	Harry Flynn	08/05/2018 11:39
Luis's copy of Differentiation: Product rule	draft	Luis Hernandez	30/11/2018 19:04
Differentiation : Product Rule	draft	Johnny Yi	08/12/2020 02:17
Standard Differentiation	draft	Heather Driscoll	11/02/2019 13:23
Heather's copy of Differentiation : Product Rule	draft	Heather Driscoll	11/02/2019 13:14
Heather's copy of Differentiation : Product Rule	draft	Heather Driscoll	11/02/2019 13:22
Standard Integration	draft	Heather Driscoll	11/02/2019 13:59
Standard Differentiation (Trig)	draft	Heather Driscoll	01/03/2019 12:20
Standard Differentiation (Trig2)	draft	Heather Driscoll	21/09/2022 16:14
JD's copy of Differentiation: Product rule	draft	JD Ichwan	21/05/2019 05:38

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Question statement

Differentiate the following function $f(x)$ using the product rule.

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	5
s1	integer	1
b	integer	4
m	integer	3
n	integer	5

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random(2..9)

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Generated value: `integer`

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Advice
"Unnamed part" - prompt
"Unnamed part" → "Unnamed gap" - Correct answer

Parts

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1. Gap Mathematical expression
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Gap-fill

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$\displaystyle \simplify[std]{f(x) = x ^ {m} * ({a} * x+{b})^{n}}$

$\displaystyle \frac{df}{dx}=\;$ Unnamed gap

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Advice

The product rule says that if $u$ and $v$ are functions of $x$ then

$\simplify[std]{Diff(u * v,x,1) = u * Diff(v,x,1) + v * Diff(u,x,1)}$

For this example:

$\simplify[std]{u = x ^ {m}}\Rightarrow \simplify[std]{Diff(u,x,1) = {m}x ^ {m -1}}$

$\simplify[std]{v = ({a} * x+{b})^{n}} \Rightarrow \simplify[std]{Diff(v,x,1) = {n*a} * ({a} * x+{b})^{n-1}}$

Hence on substituting into the product rule above we get:

$\simplify[std]{Diff(f,x,1) = {m}x ^ {m-1} * ({a} * x+{b})^{n}+{n*a}x^{m} * ({a} * x+{b})^{n-1}}$

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Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

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Generated value: `integer`

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Differentiation: Product rule

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`