2024 CJC Promo Q5

2024 CJC Promo Q5

6 marks

Promo

Differentiate each of the following expressions with respect to \(x\).

\({{\tan }^{-1}}\sqrt{2+{{x}^{3}}}\)[3]
\(\ln \left( \frac{x}{\sqrt{1-x}} \right)\)[3]

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Answer:(a) \(\frac{3x^2}{2(3+x^3)\sqrt{2+x^3}}\) (b) \(\frac{1}{x} + \frac{1}{2(1-x)}\)

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