Product 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
Product rule	draft	Frank Doheny	18/11/2016 11:36
Katy's copy of Product rule	Ready to use	Katy Dobson	30/07/2018 12:49
Katy's copy of Katy's copy of Product rule	Ready to use	Katy Dobson	30/07/2018 13:38
Product rule	draft	Xiaodan Leng	10/07/2019 23:39
Product rule	draft	Xiaodan Leng	10/07/2019 23:40

Question statement

Differentiate the function

$f(x)=(\var{a1}x^\var{a2}+\var{a3})e^{\var{a4}x+\var{a5}}$

Give any introductory information the student needs.

			Name	Type	Generated Value

a1	integer	2
a2	integer	4
a3	integer	7
a4	integer	4
a5	integer	15

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A random number between and (inclusive) with step size

Description

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Generated value: `integer`

Parts

Gap-fill
1. Gap Mathematical expression
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Gap-fill

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

Advice

$f(x)=(\var{a1}x^\var{a2}+\var{a3})e^{\var{a4}x+\var{a5}}$

Recall the product rule if $f(x)=u.v$ where $u$ and $v$ are both functions of $x$ then

$\frac{df}{dx}=v.\frac{du}{dx}+u.\frac{dv}{dx}$

let $u=\var{a1}x^\var{a2}+\var{a3}$ and $v=e^{\var{a4}x+\var{a5}}$

$\frac{du}{dx}=\var{a2}*\var{a1}x^{\var{a2}-1}$ and $\frac{dv}{dx}=\var{a4}*e^{\var{a4}x+\var{a5}}$

$\frac{df}{dx}=e^{\var{a4}x+\var{a5}}*\var{a2}*\var{a1}x^{\var{a2}-1}+(\var{a1}x^\var{a2}+\var{a3})*\var{a4}*e^{\var{a4}x+\var{a5}}$

$\frac{df}{dx}=\simplify{e^({a4}x+{a5})*{a1}*{a2}x^{{a2}-1}+({a1}x^{a2}+{a3})*{a4}*e^({a4}x+{a5})}$

$\frac{df}{dx}=(\simplify{{a1}*{a4}x^{a2}+{a1}*{a2}x^{{a2}-1}+{a3}*{a4}})\simplify{e^({a4}x+{a5})}$

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Taxonomy: mathcentre

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Taxonomy: Context

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Checkpoint description

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`

Parts

Gap-fill

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Product 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`