diff by quotient rule

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Johnny Yi 6 years, 4 months ago

Created this as a copy of Luis's copy of Differentiation: Quotient rule.

Name	Status	Author	Last Modified
Differentiation: Quotient rule	draft	Newcastle University Mathematics and Statistics	20/11/2019 14:50
DOCE UNO Derivadas cociente	draft	Marlon Arcila	08/09/2021 00:42
Luis's copy of Differentiation: Quotient rule	draft	Luis Hernandez	30/11/2018 18:59
diff by quotient rule	draft	Johnny Yi	19/12/2018 01:11

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Question statement

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

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	3
c	integer	8
b	integer	3
d	integer	1
s2	integer	1
s1	integer	1
det	integer	-21
c1	integer	8

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Description

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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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1. Step Information only

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

$\simplify[std]{f(x) = ({a} * x+{b})/({c}x^2+{d})}$
You are given that

$\frac{df}{dx}=\simplify[std]{g(x)/({c}x^2+{d})^2}$
for a polynomial

$g(x)$ . You are asked to find

$g(x)$

$g(x)=\;$ Unnamed gap

Input all numbers as fractions or integers and not as decimals.

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Advice

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

$\simplify[std]{Diff(u/v,x,1) = (v * Diff(u,x,1) - u * Diff(v,x,1))/v^2}$

For this example:

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

$\simplify[std]{v = ({c} * x^2+{d})} \Rightarrow \simplify[std]{Diff(v,x,1) = {2*c}x}$

Hence on substituting into the quotient rule above we get:

$\begin{eqnarray*} \frac{df}{dx}&=&\simplify[std]{({a}({c}x^2+{d})-{2*c}x({a}x+{b}))/({c}x^2+{d})^2}\\ &=&\simplify[std]{({a*c}x^2+{a*d}-{2*c*a}x^2-{2*c*b}x)/({c}x^2+{d})^2}\\ &=&\simplify[std]{({-c*a}x^2+{-2*b*c}x+{a*d})/({c}x^2+{d})^2} \end{eqnarray*}$
Hence

$g(x)=\simplify[std]{{-c*a}x^2+{-2*b*c}x+{a*d}}$

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Johnny Yi 6 years, 4 months ago

Error in variable testing condition

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Generated value: `integer`

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diff by quotient rule

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Johnny Yi 6 years, 4 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`