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Methods2026 NHT Exam 1 · Q1Tech-free4 marks

Product rule with a logarithm; antiderivative with a boundary condition

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a.

Let $y = x^3 \log_e(5x)$ .

Find $\dfrac{dy}{dx}$ .

2 marks

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b.

Let $f'(x) = (x-2)^3$ .

Find $f(x)$ , where $f(1) = 1$ .

2 marks

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