Answer 1

\[\frac{d}{dx}\left( \frac{1}{\sin x} + 2^{x + 3} + \frac{4}{\log_x 3} \right)\]
\[ = \frac{d}{dx}\left( \cos ec x + 2^x . 2^3 + \frac{4}{\frac{\log 3}{\log x}} \right)\]
\[ = \frac{d}{dx}\left( \cos ec x \right) + 2^3 \frac{d}{dx}\left( 2^x \right) + \frac{4}{\log 3}\frac{d}{dx}\left( \log x \right)\]
\[ = - \cos ec x cot x + 2^3 . 2^x . \log 2 + \frac{4}{\log 3} . \frac{1}{x}\]
\[ = - \cos ec x cot x + 2^{x + 3} . \log 2 + \frac{4}{x\log 3}\]