Find $\frac{\mathrm{d}}{\mathrm{d}x}x{{\tan }^{-1}}\left( 2x \right)$.[3] Find \(\frac{\mathrm{d}}

Question

Find $\frac{\mathrm{d}}{\mathrm{d}x}x{{\tan }^{-1}}\left( 2x \right)$.[3] Find $\frac{\mathrm{d}}{\mathrm{d}x}\ln \left( \sqrt{\frac{{{x}^{2}}+1}{x}} \right)$, leaving your answer as a single fraction.[3]

Accepted Answer

(a) $\frac{2x}{1 + 4x^2} + \tan^{-1}(2x)$ (b) $\frac{x^2 - 1}{2x(x^2 + 1)}$

2023 CJC Promo Q2

2023 CJC Promo Q2

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