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6
6(1)².
A Level · English Medium · Cambridge · Mathematics
Equations, patterns and functions
Apply product/chain rules, integration and stationary-point tests.
About this lesson and its coverage
Original Kidemy A Level progression. This level has its own text, examples and questions. Curriculum versions share the progression; complete board-specific coverage still needs specification matching and additional material.
Learn the idea
Differentiation rules follow how a function is built. The chain rule accounts for the inside rate; the product rule has two terms. A zero first derivative is a candidate needing a sign or curvature test. Integration must include bounds or a constant as appropriate.
Worked example
For y=(2x+1)^3, y′=6(2x+1)². For y=xe^x, y′=e^x+xe^x. A definite integral has no free additive constant in its evaluated value.
- Identify the quantities and restrictions.
- Show a method with units or symbols.
- Check and explain the result.
Your written practice
Show your working on paper. Check your answer, then choose Next.
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16
[x^4]0 to 2.
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2
3x²−12=0 gives±2.
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2x ln x+x.
Use the product rule and derivative1/x.
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It is stationary but neither a local maximum nor minimum; the derivative is positive on both sides except at 0.
Do not treat y″=0 as a classification.
Progress and browser storage
Notebook challenge, sources and further study
Apply the idea
Analyse one function using its derivative, a sign check and a definite integral.
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- Use the stated evidence or givens.
- Show reasoning rather than only a result.
- Review and explain one correction.
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