A) \[\frac{{{\log }_{2}}e}{x\,lnx}\]
B) \[\frac{2.3026}{x\ln \,\,xln\,2}\]
C) \[\frac{1}{ln{{(2x)}^{x}}}\]
D) None of these
Correct Answer: A
Solution :
\[y={{\log }_{2}}\{{{\log }_{2}}(x)\}={{\log }_{2}}\{{{\log }_{e}}x.{{\log }_{2}}e\}\] \[\Rightarrow y={{\log }_{e}}\{{{\log }_{e}}x.{{\log }_{2}}e\}.{{\log }_{2}}e\] \[\Rightarrow \] \[\frac{dy}{dx}={{\log }_{2}}e\frac{d}{dx}[{{\log }_{e}}\{{{\log }_{e}}x.{{\log }_{2}}e\}]\] \[\Rightarrow \] \[\frac{dy}{dx}={{\log }_{2}}e.\frac{1}{{{\log }_{e}}x.{{\log }_{2}}e}.({{\log }_{e}}x.{{\log }_{2}}e)\] \[\Rightarrow \] \[\frac{dy}{dx}=\frac{1}{{{\log }_{e}}x}{{\log }_{2}}=\frac{{{\log }_{2}}e}{x\ln x}\]
You need to login to perform this action.
You will be redirected in
3 sec
