Differentiation — A-Level Mathematics Revision
Revise Differentiation for A-Level Mathematics. Step-by-step explanation, worked examples, common mistakes and exam-style practice aligned to AQA, Edexcel and OCR.
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Go to IntegrationWhat is Differentiation?
Differentiation at A-Level is the process of finding the derivative or gradient of a function. It involves using standard rules to differentiate various functions, including polynomials, trigonometric functions, exponentials, and logarithms. You will also learn the chain, product, and quotient rules for more complex functions.
Board notes: All A-Level Maths boards (AQA, Edexcel, OCR) cover differentiation in a similar manner. The complexity of the functions to be differentiated and the applications of differentiation (e.g., optimisation problems) may vary slightly.
Step-by-step explanationWorked example
Differentiate y = x²sin(x). Using the product rule, dy/dx = u(dv/dx) + v(du/dx), where u = x² and v = sin(x). So, du/dx = 2x and dv/dx = cos(x). Therefore, dy/dx = x²cos(x) + 2xsin(x).
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Common mistakes
- 1Forgetting to apply the chain rule when differentiating a composite function, such as (2x+3)^5.
- 2Confusing the product and quotient rules. It's important to use the correct formula for each situation.
- 3Making errors when differentiating trigonometric functions, such as mixing up the derivatives of sin(x) and cos(x).
Differentiation exam questions
Exam-style questions for Differentiation with mark-scheme style solutions and timing practice. Aligned to AQA, Edexcel and OCR specifications.
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Step-by-step method
Step-by-step explanation
4 steps · Worked method for Differentiation
Core concept
Differentiation at A-Level is the process of finding the derivative or gradient of a function. It involves using standard rules to differentiate various functions, including polynomials, trigonometric…
Frequently asked questions
What is the second derivative?
The second derivative of a function is found by differentiating the function twice. It tells us about the concavity of the function's graph and can be used to find points of inflection.
How do I find the equation of a tangent to a curve?
To find the equation of a tangent to a curve at a given point, you first need to find the gradient of the curve at that point by differentiating. Then, use the point and the gradient in the formula y - y1 = m(x - x1).