A) \[\frac{1}{x{{\log }_{e}}10}-\frac{{{\log }_{e}}10}{x{{({{\log }_{e}}x)}^{2}}}\]
B) \[\frac{1}{x{{\log }_{e}}10}-\frac{1}{x{{\log }_{10}}e}\]
C) \[\frac{1}{x{{\log }_{e}}10}-\frac{{{\log }_{e}}10}{x{{({{\log }_{e}}x)}^{2}}}\]
D) None of these
Correct Answer: A
Solution :
\[y={{\log }_{10}}x+{{\log }_{x}}10+{{\log }_{x}}x+{{\log }_{10}}10\] \[={{\log }_{10}}x+\frac{{{\log }_{e}}10}{\log x}+1+1\] \[\Rightarrow \frac{dy}{dx}=\frac{1}{x}{{\log }_{10}}e-\frac{{{\log }_{e}}10}{x{{({{\log }_{e}}x)}^{2}}}\].
You need to login to perform this action.
You will be redirected in
3 sec
