A) \[\frac{{{2}^{\log x}}}{\log 2}\]
B) \[{{2}^{\log x}}.\log 2\]
C) \[\frac{{{2}^{\log x}}}{x}\]
D) \[\frac{{{2}^{\log x}}.\log 2}{x}\]
Correct Answer: D
Solution :
Given, \[y={{2}^{\log x}}\] \[\Rightarrow \] \[\frac{dy}{dx}={{2}^{\operatorname{logx}}}.{{\log }_{e}}2.\frac{1}{x}\] \[\left[ \because \,\frac{d}{dx}({{a}^{x}})={{a}^{x}}{{\log }_{e}}a \right]\] \[\Rightarrow \] s\[\frac{dy}{dx}=\frac{{{2}^{\log x}}.{{\log }_{e}}2}{x}\]
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