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JEE Main & Advanced Mathematics Differentiation Question Bank Derivative at a point Standard Differentiation

  • question_answer
    \[\frac{d}{dx}({{\log }_{e}}x)({{\log }_{a}}x)]=\]                          

    A)            \[\frac{{{\log }_{a}}x}{x}\]

    B)  \[\frac{{{\log }_{x}}x}{x}\]

    C)            \[\frac{2\log x}{x}\]

    D)            \[\frac{2{{\log }_{a}}x}{x}\]

    Correct Answer: D

    Solution :

               \[\frac{d}{dx}\left( {{\log }_{e}}x.{{\log }_{a}}x \right)=\frac{d}{dx}\left[ \log x.\frac{\log x}{\log a} \right]\]                                                \[=\frac{2\log x}{x.\log a}=\frac{2{{\log }_{a}}x}{x}\].


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