Power Rule 01

Error

There was an error loading the page.

Contributors

Michael Proudman

History

○

Michael Proudman 3 years, 5 months ago

Published this.

○

Michael Proudman 3 years, 5 months ago

Created this.

Name	Status	Author	Last Modified
Power Rule 01	draft	Michael Proudman	28/04/2023 15:24
Power Rule 02	draft	Michael Proudman	07/12/2021 15:19
Power Rule 03	draft	Michael Proudman	08/12/2021 09:15

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

Question statement

The Power Rule

You can find the derivative for powers of functions using the following rule:

If $y=ax^n$ then $\frac{dy}{dx} = n \times a x^{n-1}$

The Sum or Difference Rules

The derivative of $f(x) + g(x)$ is $\frac{df}{dx} + \frac{dg}{dx}$ and the derivative of $f(x) - g(x)$ is $\frac{df}{dx} - \frac{dg}{dx}$

Give any introductory information the student needs.

			Name	Type	Generated Value

a_1	integer	6
n_1	integer	6
a_2	integer	10
n_2	integer	8
a_3	integer	-4
n_3	integer	-3

Automatically regenerate variables?

Name

Data type

Value

A random number between and (inclusive) with step size

Description

Co-efficient for Q1

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`

→ Used by:

This variable doesn't seem to be used anywhere.

Parts

Information only
Part a) Gap-fill
1. Gap Mathematical expression
  Add
Part b) Gap-fill
1. Gap Mathematical expression
  Add
Part c) Gap-fill
1. Gap Mathematical expression
  Add

Information only

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

Differentiate the following:

Advice

We are asked to differentiate a variety of functions, each consisting of a single term.

We can do this using the "Power Rule" for differentiation:

If $y=ax^n$ then $\frac{dy}{dx} = n \times a x^{n-1}$

In plain language, "multiply by the power, then reduce the power by one".

Then:

$y= \var{a_1} x^{\var{n_1}}$

$\frac{dy}{dx } = \var{n_1} \times \var{a_1} x^{\var{n_1} - 1}$

$\frac{dy}{dx } = \simplify{ {n_1}*{a_1}*x^{{n_1} - 1} }$

$y= \var{a_2} x^{\var{n_2}}$

$\frac{dy}{dx } = \var{n_2} \times \var{a_2} x^{\var{n_2} - 1}$

$\frac{dy}{dx } = \simplify{ {n_2}*{a_2}*x^{{n_2} - 1} }$

$y= \var{a_3} x^{\var{n_3}}$

$\frac{dy}{dx } = \var{n_3} \times \var{a_3} x^{\var{n_3} - 1}$

$\frac{dy}{dx } = \simplify{ {n_3}*{a_3}*x^{{n_3} - 1} }$

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?
Information only
Gap-fill
Gap-fill		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet

This question is used in the following exams:

Loading...

Error

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Michael Proudman 3 years, 5 months ago

Michael Proudman 3 years, 5 months ago

The Power Rule

The Sum or Difference Rules

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Information only

Loading...

Error

Power Rule 01

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Michael Proudman 3 years, 5 months ago

Michael Proudman 3 years, 5 months ago

The Power Rule

The Sum or Difference Rules

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Information only

Generated value: `integer`