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Methods2025 NHT Exam 1 · Q1Tech-free4 marks

Derivative of a log quotient and a composite sine

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a.

Let $y = \dfrac{\log_e(x)}{x^3}$ .

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

2 marks

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b.

Let $f(x) = \sin\left(\pi e^{3x}\right)$ .

Evaluate $f'(0)$ .

2 marks

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