Harry's copy of Blathnaid's copy of Differentiate product of trig function and binomial

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Harry Flynn

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Harry Flynn 6 years, 11 months ago

Created this as a copy of Blathnaid's copy of Differentiate product of trig function and binomial.

Name	Status	Author	Last Modified
Differentiate product of trig function and binomial	draft	Newcastle University Mathematics and Statistics	20/11/2019 14:50
Blathnaid's copy of Differentiate product of trig function and binomial	draft	Blathnaid Sheridan	28/02/2020 11:15
Harry's copy of Blathnaid's copy of Differentiate product of trig function and binomial	draft	Harry Flynn	08/05/2018 12:29
Luis's copy of Differentiate product of trig function and binomial	draft	Luis Hernandez	30/11/2018 19:04
Differentiate product of trig function and binomial	Ready to use	Simon Vaughan	20/08/2020 13:00

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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	4
s1	integer	-1
b	integer	-4
m	integer	7
n	integer	2

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(1..4)

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

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Generated value: `integer`

→ Used by:

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

Parts

Gap-fill
1. Gap Mathematical expression
  Add

Gap-fill

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

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

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

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:

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

$\simplify[std]{v = sin({n} * x)} \Rightarrow \simplify[std]{Diff(v,x,1) = {n} * cos({n} * x)}$

Hence on substituting into the product rule above we get:

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

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Harry's copy of Blathnaid's copy of Differentiate product of trig function and binomial

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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History

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Checkpoint description

Harry Flynn 6 years, 11 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Loading...

Error

Harry's copy of Blathnaid's copy of Differentiate product of trig function and binomial

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Harry Flynn 6 years, 11 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`