Differentiating powers of x

Error

There was an error loading the page.

Contributors

Dann Mallet

History

○

Dann Mallet 8 years, 7 months ago

Published this.

○

Dann Mallet 8 years, 7 months ago

Created this.

Name	Status	Author	Last Modified
Differentiating powers of x	draft	Dann Mallet	14/09/2016 14:57
Differentiating powers of x	draft	Nigel Atkins	06/04/2020 12:28
Harry's copy of Differentiating powers of x	draft	Harry Flynn	08/05/2018 12:26

Question statement

This question provides you with practice at developing your ability to apply rules for differentiating polynomials. You may wish to check out this video first as it will help you to attack these problems.

Give any introductory information the student needs.

			Name	Type	Generated Value

a0	integer	5
a1	integer	5
a2	integer	-4
a3	integer	4
a4	integer	-1
e1	integer	3
e2	integer	5
e3	integer	7

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(1..5)*random(1,-1)

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`

Advice

This question is essentially testing your learning of how to differentiate polynomials.

a) the derivative of a constant by itself is always zero.

b) the derivative of a constant multiplied by $x$ is always just that constant. Here this means $f'(x)=\var{a1}$ .

c) the derivative of a sum is the sum of the individual terms' derivatives. This question has a sum made up of a constant and a constant multiple of $x$ , so you use approach taken for a and b and then add the results. Here we have

$r'(t)=(\var{a0})'+(\var{a1}t)'=0+\var{a1}=\var{a1}$

d) the derivative of a constant multiple of a power of the variable (here $t$ ) is the constant multiplied by the power, then multiplied by the variable to one power fewer. That is,

$s'(t)=(\var{a2})(\var{e3})t^{\var{e3}-1}=\simplify{{a2}{a3}t^({e3}-1)}.$

e) combining the approach taken for all of the above allows you to differentiate the final polynomial. Find the derivative of each individual term, then add the results to give the derivative of the function as a whole.

$\frac{\mathrm{d}y}{\mathrm{d}x}=\var{a1}+(\var{e1})(\var{a2})x^{\var{e1}-1}+(\var{e2})(\var{a3})x^{\var{e2}-1}=\simplify{{a1}+{e1}{a2}x^({e1}-1)+{e2}{a3}x^({e2}-1)}$

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Mathematical expression
Mathematical expression		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet

This question is not used in any exams.

Loading...

Error

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Dann Mallet 8 years, 7 months ago

Dann Mallet 8 years, 7 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Mathematical expression

Advanced settings

Checking accuracy

Variable value generators

Pattern restriction

Variables

String restrictions

Loading...

Error

Differentiating powers of x

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Dann Mallet 8 years, 7 months ago

Dann Mallet 8 years, 7 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Mathematical expression

Advanced settings

Checking accuracy

Variable value generators

Pattern restriction

Variables

String restrictions

Generated value: `integer`