Fun with Differentiation and Tangents: OCR MEI Maths for A Level Students!

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Niamh Cooke

30/03/2023

Maths

Differentiation

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Maths

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Differentiation

Fun with Differentiation and Tangents: OCR MEI Maths for A Level Students!

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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 equations of tangents and normals, determining stationary points, and using differentiation for optimization problems. Integration involves calculating definite integrals, finding volumes of revolution, and applying the trapezium rule. Understanding these concepts is crucial for success in OCR MEI A Level Mathematics Exam Practice.

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30/03/2023

237

Differentiation
(a) uses
1y = ax
1
+
gradient of a cure at a specific paint.
opposite of integration
"
(c) know how to prove differentiation

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Advanced Differentiation Techniques

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/ $2√x$ .

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 $du/dx$ + u $dv/dx$ .

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.

View

Advanced Differentiation and Integration Techniques

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 = $v(du/dx$ - u $dv/dx$ ) / v².

Example: For y = $x² + 1$ / $3x - 1$ , apply the Quotient Rule to find dy/dx = $2x(3x-1$ - 3 $x²+1$ ) / $3x-1$ ².

Differentiating inverse functions and exponential functions are also covered. For exponential functions, remember that d/dx $eˣ$ = 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 $ln|x|$ = 1/x.

These advanced techniques are crucial for solving complex problems in OCR MEI Maths A Level topic questions and exams.

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Subjects

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Pure maths

Differentiation

Maths

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237

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30 Mar 2023

•

3 pages

Fun with Differentiation and Tangents: OCR MEI Maths for A Level Students!

Niamh Cooke

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Advanced Differentiation Techniques

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/ $2√x$ .

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 $du/dx$ + u $dv/dx$ .

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.

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Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Advanced Differentiation and Integration Techniques

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 = $v(du/dx$ - u $dv/dx$ ) / v².

Example: For y = $x² + 1$ / $3x - 1$ , apply the Quotient Rule to find dy/dx = $2x(3x-1$ - 3 $x²+1$ ) / $3x-1$ ².

Differentiating inverse functions and exponential functions are also covered. For exponential functions, remember that d/dx $eˣ$ = 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 $ln|x|$ = 1/x.

These advanced techniques are crucial for solving complex problems in OCR MEI Maths A Level topic questions and exams.

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 Fundamentals

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 $x - x₁$ , 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 $+C$ 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 $y₀ + yn + 2(y₁ + y₂ + ... + yn-1)$ , where h is the strip width.

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Fun with Differentiation and Tangents: OCR MEI Maths for A Level Students!

Advanced Differentiation Techniques

Advanced Differentiation and Integration Techniques

Similar content

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

Knowunity is the #1 education app in five European countries

Knowunity has been named a featured story on Apple and has regularly topped the app store charts in the education category in Germany, Italy, Poland, Switzerland, and the United Kingdom. Join Knowunity today and help millions of students around the world.

4.9+

21 M

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Still not convinced? See what other students are saying...

I love this app so much, I also use it daily. I recommend Knowunity to everyone!!! I went from a D to an A with it :D

The app is very simple and well designed. So far I have always found everything I was looking for :D

I love this app ❤️ I actually use it every time I study.

Fun with Differentiation and Tangents: OCR MEI Maths for A Level Students!

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Advanced Differentiation Techniques

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Advanced Differentiation and Integration Techniques

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Differentiation Fundamentals

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