cormac's copy of Quotient rule

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cormac breen

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cormac breen 8 years, 1 month ago

Created this as a copy of Quotient rule.

Name	Status	Author	Last Modified
Quotient rule	draft	Frank Doheny	18/11/2016 11:36
cormac's copy of Quotient rule	draft	cormac breen	04/03/2017 17:43
cormac's copy of cormac's copy of Quotient rule	draft	cormac breen	04/03/2017 18:03
Katy's copy of Quotient rule	Ready to use	Katy Dobson	30/07/2018 12:51
Quotient rule	draft	Xiaodan Leng	10/07/2019 23:39
Quotient rule	draft	Xiaodan Leng	10/07/2019 23:39

Question statement

Differentiate the function:

$f(x)=\frac{\var{a}x^{\var{b}}+\var{f}}{\var{c}cos(\var{d}x)}$

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	7
b	integer	4
c	integer	6
f	integer	7
d	integer	6

Automatically regenerate variables?

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Data type

Value

A random number between and (inclusive) with step size

Description

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

Can an exam override the value of this variable?

Generated value: `integer`

→ Used by:

Statement
Advice
"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.

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

Advice

$f(x)=\frac{\var{a}x^{\var{b}}+\var{f}}{\var{c}cos(\var{d}x)}$

Recall the quotient rule: if $y=\frac{u}{v}$ where $u$ and $v$ are both functions of $x$ then

$\frac{dy}{dx}=\frac{v\frac{du}{dx}-u\frac{dv}{dx}}{v^2}$

Let $u=\var{a}x^{\var{b}}+\var{f}$ and $v=\var{c}cos(\var{d}x)$

then $\frac{du}{dx}=\var{b}*\var{a}x^{\var{b}-1}$ and $\frac{dv}{dx}=-\var{d}*\var{c}sin(\var{d}x)$

Putting these results together as shown in the rule gives:

$\frac{df}{dx}=\frac{(\var{c}cos(\var{d}x))*\var{b}*\var{a}x^{\var{b}-1}-(\var{a}x^{\var{b}}+\var{f})*(-\var{d}*\var{c}sin(\var{d}x))}{(\var{c}cos(\var{d}x))^2}$

$\frac{df}{dx}=\frac{\simplify{({c}*cos({d}x))*{b}*{a}x^{{b}-1}+({a}x^{{b}}+{f})*({c}*{d}*sin({d}x))}}{(\var{c}*cos(\var{d}x))^2}$

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Taxonomy: mathcentre

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cormac breen 8 years, 1 month ago

Error in variable testing condition

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Warning

Generated value: `integer`

Parts

Gap-fill

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cormac's copy of Quotient rule

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

cormac breen 8 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`