Implicit Differentiation

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Clare Lundon

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Clare Lundon 9 years, 6 months ago

Created this as a copy of SFY0004 Implicit 1.

Name	Status	Author	Last Modified
SFY0004 Implicit 1	Ready to use	Bill Foster	01/06/2016 09:47
Implicit Differentiation	draft	Clare Lundon	16/01/2018 13:19
Implicit 1	draft	Violeta CIT	26/09/2016 15:15
Simon's copy of SFY0004 Implicit 1	draft	Simon Thomas	11/03/2019 14:41
Harder implicit differentiation	draft	Simon Thomas	11/03/2019 15:41
Implicit 1	draft	Xiaodan Leng	11/07/2019 06:39

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Question statement

Given the implicit function:

$\simplify[all,!collectNumbers]{x^2+y^2-{a}x*y+{b}y}=\var{c}$

find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$ , assuming that $y$ is a function of $x$ .

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			Name	Type	Generated Value

a	integer	5
c	integer	1
b	integer	7

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1. Gap Mathematical expression
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Input your answer here: $\displaystyle \frac{dy}{dx}=$ Unnamed gap

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$\simplify[all,!collectNumbers]{x^2+y^2-{a}x*y+{b}y}=\var{c}$

On differentiating both sides of the equation implicitly we get

$2x + \simplify[all,!collectNumbers]{2y*Diff(y,x,1) - [{a}x*Diff(y,x,1)+{a}y] + {b} *Diff(y,x,1)} = 0$
Collecting terms in

$\displaystyle\dfrac{dy}{dx}$ and rearranging the equation we get

$(\var{b} -\var{a}x+ 2y) \dfrac{dy}{dx} = \simplify[all,!collectNumbers]{{a}y -2x}$ and hence on further rearranging:

$\frac{dy}{dx} = \simplify{({a}y - 2 * x) / ({b} -{a}x +(2 * y))}$

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Taxonomy: mathcentre

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Clare Lundon 9 years, 6 months ago

Error in variable testing condition

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Generated value: `integer`

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Implicit Differentiation

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Clare Lundon 9 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`