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J
Jenni
03/09/2025
Maths
GCSE AQA Further Maths Differentiation
426
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3 Sept 2025
โข
Easy AQA Further Maths GCSE: Differentiation Fun & Practice with Past Papers
J
Jenni
@jennii007
1 / 2
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[hโ0] (f(x+h) - f(x)) / h
Example: For f(x) = 3x^2, we can find f'(x) by calculating: f'(x) = lim[hโ0] (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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The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
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This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
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Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because itโs too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
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
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didnโt even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as Iโm sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH ๐๐๐ฒ๐ค๐โจ๐๐ฎ
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because itโs too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
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
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didnโt even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as Iโm sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH ๐๐๐ฒ๐ค๐โจ๐๐ฎ
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
Easy AQA Further Maths GCSE: Differentiation Fun & Practice with Past Papers
J
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
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[hโ0] (f(x+h) - f(x)) / h
Example: For f(x) = 3x^2, we can find f'(x) by calculating: f'(x) = lim[hโ0] (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 youโd never ask...
What is the Knowunity AI companion?
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
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 โ all at your fingertips.
Can't find what you're looking for? Explore other subjects.
Students love us โ and so will you.
4.9/5
App Store
4.8/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because itโs too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
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
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didnโt even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as Iโm sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH ๐๐๐ฒ๐ค๐โจ๐๐ฎ
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because itโs too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
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
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didnโt even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as Iโm sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH ๐๐๐ฒ๐ค๐โจ๐๐ฎ
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user