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237
•
30 Mar 2023
•
Niamh Cooke
@niamhcooke_yelp
Differentiation and integration are fundamental concepts in OCR MEI Maths... Show more
This page delves into more complex differentiation topics for OCR MEI A Level Maths.
Negative and fractional powers require special attention when differentiating. For example, when differentiating y = √x, it becomes dy/dx = 1/.
Second-order differentiation involves differentiating twice and is useful for identifying the nature of stationary points.
Example: If d²y/dx² > 0, the point is a minimum; if d²y/dx² < 0, it's a maximum.
The page introduces the Chain Rule, used when there's a function inside another function. It's often applied in rates of change problems.
Definition: The Chain Rule states that dy/dx = dy/du × du/dx, where u is the inner function.
The Product Rule is used when two functions are multiplied together. Its formula is dy/dx = v + u.
Highlight: When sketching gradient functions, remember that concave upwards indicates d²y/dx² > 0, while concave downwards means d²y/dx² < 0.
The page also covers differentiating exponential functions and provides standard results that students must learn for the OCR MEI Maths A Level exam.
This final page covers advanced topics in differentiation and integration for OCR MEI A Level Maths.
The Quotient Rule is introduced for differentiating fractions of functions. The formula is dy/dx = - u) / v².
Example: For y = / , apply the Quotient Rule to find dy/dx = - 3) / ².
Differentiating inverse functions and exponential functions are also covered. For exponential functions, remember that d/dx = eˣ.
Highlight: When differentiating trigonometric functions, ensure angles are in radians.
Implicit differentiation is explained, which is useful when differentiating equations with two variables, typically x and y.
Tip: In implicit differentiation, when differentiating with respect to x, add dy/dx to terms containing y.
The page concludes with natural logarithms and their derivatives. For example, d/dx = 1/x.
These advanced techniques are crucial for solving complex problems in OCR MEI Maths A Level topic questions and exams.
This page covers the essential aspects of differentiation in OCR MEI Maths A Level.
Differentiation is used to find the gradient of a curve at a specific point and is the opposite of integration. Students must know how to prove differentiation from first principles and find equations of tangents and normals.
Definition: A tangent is a line that touches a curve at a single point, while a normal is perpendicular to the tangent at that point.
The nature of stationary points can be determined by finding dy/dx and evaluating points on either side of the stationary point. Differentiation is also used to calculate maximum and minimum values of functions.
Example: To find the equation of a tangent, use y - y₁ = m, where m is the gradient found through differentiation.
Integration, the opposite of differentiation, is used to calculate definite integrals and find areas under curves. When integrating, remember to include a constant for indefinite integrals.
Highlight: Always draw a sketch when calculating definite integrals to visualize where the curve crosses the axes.
The page also covers volumes of revolution and the Trapezium Rule for approximating areas under curves.
Vocabulary: The Trapezium Rule is expressed as Ax = ½h, where h is the strip width.
App Store
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 it’s 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 didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m 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 😍😁😲🤑💗✨🎀😮
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 it’s 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 didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m 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 😍😁😲🤑💗✨🎀😮
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
Niamh Cooke
@niamhcooke_yelp
Differentiation and integration are fundamental concepts in OCR MEI Maths A Level. Differentiation finds the gradient of a curve at a specific point, while integration calculates the area under curves. Key topics include proving differentiation from first principles, finding... Show more
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page delves into more complex differentiation topics for OCR MEI A Level Maths.
Negative and fractional powers require special attention when differentiating. For example, when differentiating y = √x, it becomes dy/dx = 1/.
Second-order differentiation involves differentiating twice and is useful for identifying the nature of stationary points.
Example: If d²y/dx² > 0, the point is a minimum; if d²y/dx² < 0, it's a maximum.
The page introduces the Chain Rule, used when there's a function inside another function. It's often applied in rates of change problems.
Definition: The Chain Rule states that dy/dx = dy/du × du/dx, where u is the inner function.
The Product Rule is used when two functions are multiplied together. Its formula is dy/dx = v + u.
Highlight: When sketching gradient functions, remember that concave upwards indicates d²y/dx² > 0, while concave downwards means d²y/dx² < 0.
The page also covers differentiating exponential functions and provides standard results that students must learn for the OCR MEI Maths A Level exam.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This final page covers advanced topics in differentiation and integration for OCR MEI A Level Maths.
The Quotient Rule is introduced for differentiating fractions of functions. The formula is dy/dx = - u) / v².
Example: For y = / , apply the Quotient Rule to find dy/dx = - 3) / ².
Differentiating inverse functions and exponential functions are also covered. For exponential functions, remember that d/dx = eˣ.
Highlight: When differentiating trigonometric functions, ensure angles are in radians.
Implicit differentiation is explained, which is useful when differentiating equations with two variables, typically x and y.
Tip: In implicit differentiation, when differentiating with respect to x, add dy/dx to terms containing y.
The page concludes with natural logarithms and their derivatives. For example, d/dx = 1/x.
These advanced techniques are crucial for solving complex problems in OCR MEI Maths A Level topic questions and exams.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page covers the essential aspects of differentiation in OCR MEI Maths A Level.
Differentiation is used to find the gradient of a curve at a specific point and is the opposite of integration. Students must know how to prove differentiation from first principles and find equations of tangents and normals.
Definition: A tangent is a line that touches a curve at a single point, while a normal is perpendicular to the tangent at that point.
The nature of stationary points can be determined by finding dy/dx and evaluating points on either side of the stationary point. Differentiation is also used to calculate maximum and minimum values of functions.
Example: To find the equation of a tangent, use y - y₁ = m, where m is the gradient found through differentiation.
Integration, the opposite of differentiation, is used to calculate definite integrals and find areas under curves. When integrating, remember to include a constant for indefinite integrals.
Highlight: Always draw a sketch when calculating definite integrals to visualize where the curve crosses the axes.
The page also covers volumes of revolution and the Trapezium Rule for approximating areas under curves.
Vocabulary: The Trapezium Rule is expressed as Ax = ½h, where h is the strip width.
App Store
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 it’s 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 didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m 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 😍😁😲🤑💗✨🎀😮
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 it’s 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 didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m 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 😍😁😲🤑💗✨🎀😮
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
