Quotient rule

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Frank Doheny

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Frank Doheny 8 years, 5 months ago

Published this.

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Frank Doheny 8 years, 7 months ago

Created this.

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	2
b	integer	4
c	integer	7
f	integer	11
d	integer	4

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A random number between and (inclusive) with step size

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Generated value: `integer`

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1. Gap Mathematical expression
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$\frac{df}{dx} =$ 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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Frank Doheny 8 years, 5 months ago

Frank Doheny 8 years, 7 months ago

Error in variable testing condition

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Generated value: `integer`

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Quotient rule

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Frank Doheny 8 years, 5 months ago

Frank Doheny 8 years, 7 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`