Differentiate each of the following expressions with respect to $x$. ${{\tan }^{-1}}\sqrt{x+1}$.

Question

Differentiate each of the following expressions with respect to $x$. ${{\tan }^{-1}}\sqrt{x+1}$.[2] $\ln \left( \frac{x+{{\mathrm{e}}^{x}}}{{{3}^{x}}} \right)$.[3]

Accepted Answer

(a) $\frac{1}{2(x+2)\sqrt{x+1}}$ (b) $\frac{1 + e^x}{x + e^x} - \ln 3$

2023 ACJC Promo Q1

2023 ACJC Promo Q1

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