cormac's copy of Blathnaid's copy of Implicit differentiation

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cormac breen

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cormac breen 8 years ago

Created this as a copy of Blathnaid's copy of Implicit differentiation.

Name	Status	Author	Last Modified
Implicit differentiation	draft	Newcastle University Mathematics and Statistics	20/11/2019 14:50
cormac's copy of Implicit differentiation	draft	cormac breen	12/06/2016 20:33
CATORCE UNO Derivacion implicita	draft	Marlon Arcila	08/09/2021 00:47
Blathnaid's copy of Implicit differentiation	draft	Blathnaid Sheridan	10/01/2017 11:58
cormac's copy of Blathnaid's copy of Implicit differentiation	draft	cormac breen	04/03/2017 17:43
cormac's copy of cormac's copy of Blathnaid's copy of Implicit differentiation	draft	cormac breen	04/03/2017 18:04
Implicit differentiation (1)	draft	Adrian Jannetta	16/08/2023 14:56
Luis's copy of Implicit differentiation	draft	Luis Hernandez	30/11/2018 18:36

There are 18 other versions that do you not have access to.

Question statement

Given the following relation between $x$ and $y$

$\simplify[all,!collectNumbers]{x^2+y^2+{a}x+{b}y}=\var{c}$
answer the following question.

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	-6
c	integer	4
b	integer	5

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
-random(1..9)

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

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Generated value: `integer`

-6

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap Mathematical expression
  Add

Gap-fill

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

Using implicit differentiation find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$ .

Input your answer here:

$\displaystyle \frac{dy}{dx}=$ Unnamed gap

Advice

On differentiating both sides of the equation implicitly we get

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

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

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

$\frac{dy}{dx} = \simplify[all,!collectNumbers]{({ - a} - 2 * x) / ({b} + (2 * y))}$

Give a worked solution to the whole question.

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cormac's copy of Blathnaid's copy of Implicit differentiation

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

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Checkpoint description

cormac breen 8 years ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Loading...

Error

cormac's copy of Blathnaid's copy of Implicit differentiation

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

cormac breen 8 years ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`