Implicit Differentiation

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From users who are not members of Gareth's workspace :

Abideet Kharel

said

Ready to use

3 years, 3 months ago

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Abideet Kharel 3 years, 3 months ago

Gave some feedback: Ready to use

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Harry Flynn was given access to the Implicit Differentiation 6 years, 7 months ago

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Gareth Woods 6 years, 7 months ago

Created this as a copy of Implicit 2.

Name	Status	Author	Last Modified
SFY0004 Implicit 2	Ready to use	Bill Foster	01/06/2016 09:47
CATORCE DOS Derivacion implicita	draft	Marlon Arcila	08/09/2021 00:47
Implicit 2	draft	Leticija Dubickaite	07/06/2018 11:23
Implicit 2	draft	Leticija Dubickaite	05/07/2018 16:52
Nick's copy of Implicit 2	draft	Nick Walker	22/06/2018 00:48
Praneetha's copy of Nick's copy of Implicit 2	draft	Praneetha Singh	28/06/2018 05:50
Implicit Differentiation	Ready to use	Gareth Woods	25/01/2022 12:32
Aoife's copy of Implicit Differentiation	draft	Aoife O'Brien	21/09/2018 12:44
Simon's copy of SFY0004 Implicit 2	draft	Simon Thomas	11/03/2019 14:58
Implicit Differentiation	draft	Kevin Bohan	05/06/2019 14:44
Implicit Differentiation	draft	Kevin Bohan	05/06/2019 14:50

There are 14 other versions that do you not have access to.

Question statement

You are given the following relation between $x$ and $y$

$\simplify{x^2+y^2+{d}x y+{a}x+{b}y}=\var{c}$
where

$y=y(x)$ . Find

$\dfrac{dy}{dx}$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	-9
c	integer	7
b	integer	6
d	integer	-2

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
-random(2..9)

JME function reference

Description

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

Can an exam override the value of this variable?

Generated value: `integer`

-9

→ Used by:

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap Mathematical expression
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Gap-fill

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Input your answer here:

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

Input all numbers as integers not as decimals.

Advice

Hint:

Note that we regard $y$ as a function of $x$ . Hence we have (using the Chain Rule): $\displaystyle \frac{d(y^2)}{dx} = 2y\frac{dy}{dx}$ . And, using the Product Rule: $\displaystyle \frac{d(xy)}{dx} = y+x\frac{dy}{dx}$ .

Now differentiate both sides of the relation with respect to $x$ . Below is a worked solution to the problem, but only look at it if you are struggling.

a) By differentiating both sides of the equation implicitly we get

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

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

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

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

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This question is used in the following exams:

Implicit Differentiation by Gareth Woods in Gareth's workspace.
1 by Hamza Shah in Hamza's workspace.

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Taxonomy: mathcentre

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Checkpoint description

Abideet Kharel 3 years, 3 months ago

Harry Flynn was given access to the Implicit Differentiation 6 years, 7 months ago

Gareth Woods 6 years, 7 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

Feedback

History

Comment

Checkpoint description

Abideet Kharel 3 years, 3 months ago

Harry Flynn was given access to the Implicit Differentiation 6 years, 7 months ago

Gareth Woods 6 years, 7 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`