Exam-style question
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For G2 differentiation, what is the safest way to differentiate a mixture of x^n, e^(kx), sin(kx), tan(kx) and ln x terms?.
- A.Match each function family to its derivative rule before simplifying.
- B.Use the power rule for ln x, e^(kx), sin(kx), cos(kx) and tan(kx).
- C.Integrate the expression first because differentiation reverses integration.
- D.Ignore constants such as k because constants never affect a derivative.
Model answer
What a good answer should say
- The correct answer is Match each function family to its derivative rule before simplifying.
- For G2, x^n uses the power rule, e^(kx) differentiates to ke^(kx), trigonometric functions require their standard derivatives and ln x differentiates to 1/x.
This answer is tied to the objective: G2 Differentiate x^n for rational values of n and related constant multiples, sums and differences; differentiate e^(kx), a^(kx), sin kx, cos kx, tan kx and related sums, differences and constant multiples; understand and use the derivative of ln x..
Explanation
Why this works
Use the explanation to connect the worked answer back to G2 Differentiate x^n for rational values of n and related constant multiples, sums and differences; differentiate e^(kx), a^(kx), sin kx, cos kx, tan kx and related sums, differences and constant multiples; understand and use the derivative of ln x..
Match each function family to its derivative rule before simplifying. is correct because G2 contains several derivative families.
A strong solution identifies whether the term is a rational power, exponential, logarithmic or trigonometric function, applies the matching derivative rule, carries constants such as k through the calculation, and then simplifies. The distractors fail because they apply one rule to every function or ignore constants that change the gradient.
Maths method check
- Topic focus: Pure Mathematics.
- Question style: practice.
- Reasoning demand: application.
- Check the operation, notation, units, and final answer form against the question before moving on.
Common mistake
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