Implicit differentiation

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Newcastle University Mathematics and Statistics

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Newcastle University Mathematics and Statistics 9 years, 2 months ago

Created this.

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	-5
c	integer	4
b	integer	4

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`

-5

→ Used by:

Statement
Advice
"Unnamed part" → "Unnamed gap" - Correct answer

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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Part	Test	Passed?
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Mathematical expression		Hasn't run yet

This question is used in the following exams:

Implicit differentiation by Newcastle University Mathematics and Statistics in Content created by Newcastle University.
Implicit differentiation by Marlon Arcila in Derivadas.
Implicit differentiation by Marlon Arcila in Derivadas.
Implicit differentiation by Marlon Arcila in Derivadas.
Implicit differentiation by Marlon Arcila in Derivadas.
Implicit differentiation by Marlon Arcila in Derivadas.
week2 by haifa abd in NEM1001.
week3 by haifa abd in NEM1001.
week4 by haifa abd in NEM1001.
week5 by haifa abd in NEM1001.
Luis's copy of Implicit differentiation by Luis Hernandez in MAT333.
Maria's copy of Implicit differentiation by Maria Aneiros in Maria's workspace.
Ann's copy of Implicit differentiation by Ann Smith in Calculus.
MID-TRIMESTER EXAM REVISION 2020 T3 by Maria Aneiros in Maria's workspace.
Differentiation rules by Anita Campbell in Anita's workspace.
Implicit Differentiation question by Kuldeep Singh in Kuldeep's workspace.
1 by Hamza Shah in Hamza's workspace.
Robert's copy of Implicit differentiation by Robert Barham in Robert's workspace.

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Taxonomy: mathcentre

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Newcastle University Mathematics and Statistics 9 years, 2 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

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`