Luis's copy of Quotient rule - differentiate quadratic over quadratic

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Luis Hernandez 6 years, 4 months ago

Created this as a copy of Quotient rule - differentiate quadratic over quadratic.

Name	Status	Author	Last Modified
Quotient rule - differentiate quadratic over quadratic	Ready to use	Newcastle University Mathematics and Statistics	20/11/2019 14:50
Luis's copy of Quotient rule - differentiate quadratic over quadratic	draft	Luis Hernandez	30/11/2018 18:24
Philip's copy of Quotient rule - differentiate quadratic over quadratic	draft	Philip Charlton	17/06/2019 08:53
Quotient rule - differentiate quadratic over quadratic	draft	Xiaodan Leng	10/07/2019 22:33

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Question statement

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

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			Name	Type	Generated Value

a	integer	7
c	integer	7
b	integer	-1
d	integer	1
s2	integer	1
s1	integer	-1
det	integer	14
c1	integer	7

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

$\simplify[std]{u = ({a}x^2+{b})}\Rightarrow \simplify[std]{Diff(u,x,1) = {2*a}x}$

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

Hence on substituting into the quotient rule above we get:

$\begin{eqnarray*} \frac{df}{dx}&=&\simplify[std]{({2*a}x({c}x^2+{d})-{2*c}x({a}x^2+{b}))/({c}x^2+{d})^2}\\ &=&\simplify[std]{({2*a*c}x^3+{2*a*d}x-{2*c*a}x^3-{2*c*b}x)/({c}x^2+{d})^2}\\ &=&\simplify[std]{({2*det}x)/({c}x^2+{d})^2} \end{eqnarray*}$
Hence

$g(x)=\simplify[std]{{2*det}x}$

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Luis's copy of Quotient rule - differentiate quadratic over quadratic

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Luis Hernandez 6 years, 4 months ago

Error in variable testing condition

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Generated value: `integer`

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Luis's copy of Quotient rule - differentiate quadratic over quadratic

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Luis Hernandez 6 years, 4 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`