Easy AQA Further Maths GCSE: Differentiation Fun & Practice with Past Papers

Jenni

06/04/2023

Maths

GCSE AQA Further Maths Differentiation

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6 Apr 2023

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Easy AQA Further Maths GCSE: Differentiation Fun & Practice with Past Papers

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Jenni

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AQA Further Maths GCSE Differentiationis a crucial topic for... Show more

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Differentiation
y=x² dy = nx²
da
dy
You CANT do dx when...
→xis in brackets
→x is in denominator
→x is in root form
The gradient function of

Advanced Differentiation Techniques and Applications

This section delves deeper into Differentiation Further Maths GCSE concepts, providing more complex examples and applications.

Highlight: Differentiation of a constant is always zero. d/dx $constant$ = 0

Let's explore a comprehensive example that demonstrates various aspects of differentiation:

a) For f $x$ = 4x^2 - 8x + 3, find the gradient when x = 3

First, we find the gradient function: f' $x$ = 8x - 8

Then, we substitute x = 3: f' $3$ = 8 $3$ - 8 = 24 - 8 = 16

Example: The gradient at x = 3 is 16

b) Find the coordinates of the point on the graph of y = f(x) where the gradient is 8

We set the gradient function equal to 8: 8x - 8 = 8 Solving this, we get x = 2

To find y, we substitute x = 2 into the original function: f $2$ = 4 $2$ ^2 - 8 $2$ + 3 = 16 - 16 + 3 = 3

Example: The coordinates are (2, 3)

c) Find the gradient of y = f $x$ at the points where the curve meets the line y = 4x - 5

We set the original function equal to the line equation: 4x^2 - 8x + 3 = 4x - 5

Solving this quadratic equation, we get x = 1 or x = 2

Now, we can find the gradients at these points using the gradient function: At x = 1: f' $1$ = 8 $1$ - 8 = 0 At x = 2: f' $2$ = 8 $2$ - 8 = 8

These examples demonstrate how to apply differentiation in various scenarios, which is crucial for AQA Further Maths GCSE past papers and Further Maths GCSE practice papers.

Differentiation Basics and Rules

Differentiation is a fundamental concept in AQA GCSE Further Maths. It involves finding the gradient function of a curve, which is crucial for various mathematical applications.

The gradient function of a curve y=f(x) is written as f'(x) or dy/dx. This function allows us to find the gradient of the curve for any value of x.

Highlight: You cannot directly differentiate when x is in brackets, in the denominator, or in root form.

For the basic form y=x^n, the differentiation rule is:

dy/dx = nx^ $n-1$

Example: For f $x$ = x^3, the gradient function f' $x$ = 3x^2

An alternative method for finding the gradient function involves using the limit definition:

f' $x$ = lim $h→0$ $f(x+h$ - f(x)) / h

Example: For f $x$ = 3x^2, we can find f'(x) by calculating: f' $x$ = lim $h→0$ $3(x+h$ ^2 - 3x^2) / h After simplification, we get f' $x$ = 6x

This page provides essential information for AQA Further Maths GCSE Differentiation questions and is crucial for AQA Further Maths GCSE revision.

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Maths

•

426

•

6 Apr 2023

•

2 pages

Easy AQA Further Maths GCSE: Differentiation Fun & Practice with Past Papers

Jenni

@jennii007

AQA Further Maths GCSE Differentiation is a crucial topic for students preparing for their exams. This summary covers key concepts, formulas, and examples to help with AQA Further Maths GCSE revision.

Differentiation is the process of finding the gradient... Show more

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Advanced Differentiation Techniques and Applications

This section delves deeper into Differentiation Further Maths GCSE concepts, providing more complex examples and applications.

Highlight: Differentiation of a constant is always zero. d/dx $constant$ = 0

Let's explore a comprehensive example that demonstrates various aspects of differentiation:

a) For f $x$ = 4x^2 - 8x + 3, find the gradient when x = 3

First, we find the gradient function: f' $x$ = 8x - 8

Then, we substitute x = 3: f' $3$ = 8 $3$ - 8 = 24 - 8 = 16

Example: The gradient at x = 3 is 16

b) Find the coordinates of the point on the graph of y = f(x) where the gradient is 8

We set the gradient function equal to 8: 8x - 8 = 8 Solving this, we get x = 2

To find y, we substitute x = 2 into the original function: f $2$ = 4 $2$ ^2 - 8 $2$ + 3 = 16 - 16 + 3 = 3

Example: The coordinates are (2, 3)

c) Find the gradient of y = f $x$ at the points where the curve meets the line y = 4x - 5

We set the original function equal to the line equation: 4x^2 - 8x + 3 = 4x - 5

Solving this quadratic equation, we get x = 1 or x = 2

Now, we can find the gradients at these points using the gradient function: At x = 1: f' $1$ = 8 $1$ - 8 = 0 At x = 2: f' $2$ = 8 $2$ - 8 = 8

These examples demonstrate how to apply differentiation in various scenarios, which is crucial for AQA Further Maths GCSE past papers and Further Maths GCSE practice papers.

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Differentiation Basics and Rules

Differentiation is a fundamental concept in AQA GCSE Further Maths. It involves finding the gradient function of a curve, which is crucial for various mathematical applications.

The gradient function of a curve y=f(x) is written as f'(x) or dy/dx. This function allows us to find the gradient of the curve for any value of x.

Highlight: You cannot directly differentiate when x is in brackets, in the denominator, or in root form.

For the basic form y=x^n, the differentiation rule is:

dy/dx = nx^ $n-1$

Example: For f $x$ = x^3, the gradient function f' $x$ = 3x^2

An alternative method for finding the gradient function involves using the limit definition:

f' $x$ = lim $h→0$ $f(x+h$ - f(x)) / h

Example: For f $x$ = 3x^2, we can find f'(x) by calculating: f' $x$ = lim $h→0$ $3(x+h$ ^2 - 3x^2) / h After simplification, we get f' $x$ = 6x

This page provides essential information for AQA Further Maths GCSE Differentiation questions and is crucial for AQA Further Maths GCSE revision.

We thought you’d never ask...

What is the Knowunity AI companion?

Where can I download the Knowunity app?

You can download the app from Google Play Store and Apple App Store.

Is Knowunity really free of charge?

That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.

Smart Tools NEW

Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines

Mock Exam

Quiz

Flashcards

Essay

Students love us — and so will you.

4.9/5

App Store

4.8/5

Google Play

Stefan S

iOS user

Samantha Klich

Android user

Anna

iOS user

Best app on earth! no words because it’s too good

Thomas R

iOS user

Basil

Android user

David K

iOS user

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

Rohan U

Android user

Xander S

iOS user

Elisha

iOS user

Paul T

iOS user

Stefan S

iOS user

Samantha Klich

Android user

Anna

iOS user

Best app on earth! no words because it’s too good

Thomas R

iOS user

Basil

Android user

David K

iOS user

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

Rohan U

Android user

Xander S

iOS user

Elisha

iOS user

Paul T

iOS user

Easy AQA Further Maths GCSE: Differentiation Fun & Practice with Past Papers

Advanced Differentiation Techniques and Applications

Differentiation Basics and Rules

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Where can I download the Knowunity app?

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Easy AQA Further Maths GCSE: Differentiation Fun & Practice with Past Papers

Sign up to see the contentIt's free!

Advanced Differentiation Techniques and Applications

Sign up to see the contentIt's free!

Differentiation Basics and Rules

We thought you’d never ask...

What is the Knowunity AI companion?

Where can I download the Knowunity app?

Is Knowunity really free of charge?

Similar content

Converting Between Fractions, Decimals, and Percentages

Maths 2020 paper 2

Maths Revision Topic List

Can't find what you're looking for? Explore other subjects.

Students love us — and so will you.

4.9/5

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