Exam-style question
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G2: A student differentiates e^(3x) as e^(3x). Explain the missing step and give the corrected derivative.
Model answer
What a good answer should say
- Apply the chain rule to the exponential function.
- The derivative of e^(3x) is not just e^(3x), because the inner function 3x has derivative 3.
- Therefore d/dx[e^(3x)] = 3e^(3x).
- A common error is differentiating the outside function while forgetting the multiplier from the inside function.
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..
This question is anchored to G2 because it tests differentiation of e^(kx) and related constant multiples. It rewards correct chain-rule reasoning and a precise final derivative.
Maths method check
- Topic focus: Pure Mathematics.
- Question style: exam_style.
- Reasoning demand: recall.
- Check the operation, notation, units, and final answer form against the question before moving on.
Common mistake
No common mistake is linked to this question yet.