Differentiate the following with respect to $x$. ${{\cos }^{-1}}\left( \sin x \right)$ where&nbs

Question

Differentiate the following with respect to $x$. ${{\cos }^{-1}}\left( \sin x \right)$ where $\frac{\pi }{2} < x < \frac{3\pi }{2}$,[2] $\ln \sqrt{\frac{{{e}^{x}}+1}{1-{{e}^{-x}}}}$[3]

Accepted Answer

(i) $1$ (ii) $\frac12\left(\frac{e^x}{e^x+1}-\frac1{e^x-1}\right)$

2012 ACJC Promo Q2

2012 ACJC Promo Q2

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